s5 \

E L E C T R O C H E M I C A L A N D C A T A L Y T I C S T U D I E S

A T E L E C T R O N - C O N D U C T I N G S U R F A C E S

by

PAUL FREUND [ C~U N i P A 3

A thesis submitted

for the degree of

DOCTOR OF PHILOSOPHY

of the

UNIVERSITY OF LONDON

Department of Chemistry,

Imperial College of Science and Technology,

London, SW7 2AY. July, 1982.

Para Rhaiza

ELECTROCHEMICAL AND CATALYTIC STUDIES

AT ELECTRON-CONDUCTING SURFACES,

Theoretical expressions have been derived for the catalytic rate (u? ) cat and the catalyst potential (E ) for redox reactions catalysed by a noble CaL

metal. The model assumed that the catalysis occurred by electron transfer

through the metal, and that the individual current-potential curves of the

reacting couples were additive. The cases considered were: (a) two

irreversible couples with partial mass transport control, and (b) two

reversible couples that remain in equilibrium at the surface.

Experimental tests of the model were made with the reaction between

ferricyanide and iodide ions in aqueous potassium nitrate solutions with

large rotating disk catalysts. On an oxide-covered platinum disk the catalysis

was found to follow all the theoretical predi ctions of case b as shown

by the dependence of u1 and E on the rotation speed of the disk, on CaE CclL

the concentration of teactants and products, and on temperature. Moreover,

E and 2Fu' agree well with the mixture potential and mixture current Cau CclL

obtained by purely electrochemical experiments.

On oxide-free platinum, iodide was irreversibly adsorbed and partially

blocked the surface for the reduction of ferricyanide in the mixed system.

Here too, the catalysis followed the electron transfer path but the additivity

principle was not obeyed.

Catalytic experiments carried out on a glassy carbon disk catalyst

fitted the rotation speed dependence predicted by case a.

Despic et al.(1979), recently claimed that a new kind of " non-faradaic"

electrocatalysis, brought about by pulsing gold and silver electrodes in the

double layer region, produced large increases in the rate of hydrolysis of

t-butyl acetate. Their experiments have been checked by a pH-stat method,

and the solvolysis of t-butyl bromide on pulsed silver electrodes has also

been investigated. No evidence to substantiate this new catalytic phenomenon

was found for either reaction.

ACKNOWLEDGEMENTS

I wish to thank warmly Dr. Michael Spiro, supervisor of this

research, for his continued support and encouragement, both academic

and moral, and also for his genuine interest in my welfare.

Thanks are also due to Miss Moira Shanahan for her promptness

and skill in the typing of this thesis.

I am grateful to CONICIT (Consejo Nacional de Investigacion

Cientifica y Tecnolo'gica), the Venezuelan organisation that supported

my studies.

w w w w v / ^

V

LIST OF CONTENTS

PAGE:

ABSTRACT iii

ACKNOWLEDGEMENTS iv

LIST OF CONTENTS v

CHAPTER I. ELECTRON TRANSFER AT INTERPHASES

1.1. General Introduction 1

1.2. Thermodynamics of the Metal/Solution Interphase 3

1.3. The Butler-Volmer Equation 6

a) Simple Electrode Reactions 6

b) Consideration of Pre-Equilibria 9

c) Tafel Approximation 11

d) Approximation at Low Overpotentials

1.4. Electrochemical Reaction Orders and Activation Energies 12

1.5. Corrections to the Butler-Volmer Equation 14

a) Effect of Mass Transport Limitations 14

b) Migration of Ions 16

c) Double Layer Effects 17

d) Adsorption 20

e) The Transfer Coefficient, a 21

CHAPTER II. THE HETEROGENEOUS CATALYSIS OF REDOX REACTIONS

II.1. Introduction 23

II.2. Quantitative Model of the Catalytic Rate 27

a) Assumptions 27

b) Case of Two Irreversible Couples 28

c) Partial Control by Mass Transport to the Catalyst 29

d) Reversible Couples 32

vi

e) Suggested Tests for the Electrochemical Mechanism 40

f) Final Comments 41

CHAPTER III. ELECTROCHEMISTRY ON PLATINUM AND GLASSY CARBON.

111.1. Introduction 44

111.2. Surface Films on Platinum 44

111.3. Electrochemistry of Fe(CN)|~/Fe(CN)t~ and of

I~/I2(l3) on Platinum 49

111.4. Surface Films on Glassy Carbon 53

111.5. Electrochemistry of Fe(CN)T/FeCCN)and I~/l7

on Glassy Carbon 54

CHAPTER IV. TECHNIQUES AND INSTRUMENTATION

IV.1. The Rotating Disk Electrode (RDE) 57

a) The Ideal RDE 57

b) The Practical Rotating Disk Electrode 61

c) Uses of the RDE 64

IV.2. Current-Voltage Curves 65

a) Steady State Recording 65

b) Potential Sweep Methods 65

IV.3. Electrochemical Instrumentation 66

a) Potentiostat 66

b) The Uncompensated Solution Resistance 69

c) Cell Design 72

CHAPTER V. THE REACTION BETWEEN FERRICYANIDE AND IODIDE IN SOLUTION

V.1. Introduction 73

V.2. Experimental 75

a) Apparatus 75

b) Chemicals 77

c) Measurement of Extinction Coefficients 77

d) Typical Homogeneous Run 78

vii

V.3. Treatment of Kinetic Data 79

V.4. Results and Discussion 82

a) Extinction Coefficients 82

b) Verification of the Value of K 84

c) Homogeneous Rate Under Various Conditions 85

CHAPTER VI. CATALYSIS ON PLATINUM (OXIDISED): STUDIES IN THE

PRESENCE OF KN03

VI.1. Introduction 93

VI.2. Materials and Methods 93

a) Platinum Rotating Disk Electrode 93

b) Pre-Conditioning 96

c) Steady-State Current-Voltage Curves 99

d) E.m.f. Measurements 103

e) Catalytic Runs 103

f) Treatment of Kinetic Data 103

VI.3. Results and Discussion 105

a) Comparison of Kinetic and Electrochemical

Experiments 105

b) Theoretical Calculation of Catalytic Rates 112

c) Effect of Reactant Concentration 112

d) Effect of High Fe(CN)g~ Concentration 113

e) Effect of High I2 Concentration 116

f) Effect of [KN03] 117

g) Effect of Temperature 119

VI.4. Conclusions 123

viii

CHAPTER VII. CATALYSIS ON PLATINUM (REDUCED)

VII.1. Introduction 129

VII.2. Experimental 129

a) Chemicals 129

b) Pre-Conditioning Procedures 129

c) Cyclic Voltammograms (CV) 131

VII.3. Results and Discussion 132

a) State of the Surface Following Pre-Conditioning 132

b) Kinetic and Electrochemical Runs 135

c) Verification of Iodine Adsorption 141

VII.4. Conclusions 144

CHAPTER VIII. CATALYSIS ON PLATINUM (OXIDISED)'. STUDIES IN

THE PRESENCE OF KC^

VIII.1. Introduction 146

VIII.2. Experimental 146

a) Chemicals 146

b) Electrolyses 146

c) Chemical Analysis of Solutions After Electrolysis 147

d) Treatment of Electrolyses Data 149

VIII.3. Results and Discussion 150

a) Preliminary Results 150

b) Experiments on the Oxidation of Iodide 158

VIII.4. Conclusions 166

CHAPTER IX. CATALYSIS ON GLASSY CARBON 168

IX.1. Introduction 168

IX.2. Experimental 169

a) The Glassy Carbon RDE 169

b) Chemicals, Experimental Arrangement and Catalytic Runs 172

c) Pre-Conditioning Procedures 172

ix

IX.3. Results and Discussion 173

a) Preliminary Results 174

b) Polishing Procedure 180

c) Long-Term Performance with AN (0.1 M H2S0*,)

Pretreatment 182

d) Comparison Between Oxidised and Reduced Catalyst 185

e) Dependence of the Catalytic Rate on the Reactant

Concentration for Disks Preconditioned by Polishing

and AN (0.1 M H2S0z,) 193

f) Dependence of the Catalytic Rate on the Concentration

of the Products 200

g) Dependence of the Catalytic Rate on Temperature 203

IX. 4. Conclusions 204

CHAPTER X. SOLVOLYSIS REACTIONS

X.l. Acid-Base Catalysis 206

a) Definition of Acid-Base Catalysis 206

b) The Hydrolysis of Esters 207

c) Measurement of Rates 210

X.2. Displacement Reactions 211

CHAPTER XI. AN INVESTIGATION OF NON-FARADAIC ELECTROCATALYSIS

XI.1. Introduction 213

XI.2. Experimental 214

a) Chemicals 214

b) Equipment 214

c) The Gold and Silver Electrodes 217

d) Experimental Procedure 218

e) Treatment of Experimental Data 220 140

f) Extracts from Despic et al.'s Experimental

Procedure 223

X

XI.3. Results and Discussion 224

a) Homogeneous Runs with t-BuOAc 224

b) Hydrolysis of t-BuOAc in the Presence of Gold and

Silver Electrodes 229

c) Homogeneous Runs with t-BuBr 234

d) Solvolysis of t-BuBr in the Presence of Gold and

Silver Electrodes 234

XI.4. Conclusions 238

APPENDIX 1 241

APPENDIX 2 244

APPENDIX 3 246

APPENDIX 4 249

REFERENCES 251

1

CHAPTER ONE

ELECTRON TRANSFER A T INTERPHASES

1.1. General Introduction.

The catalysis of redox reactions in solution is very common."'"

An electrochemical mechanism has been proposed for such catalytic 2

activity by Spiro : according to this the electron transfer between

the reactants occurs through the solid conducting phase. During the

reaction the catalyst acquires a well defined non-equilibrium potential

E which is determined by the rate of electron transfer and by CoL thermodynamic quantities. This potential can be measured against any

suitable reference electrode. This model can be predictive if the 3

additivity principle of Wagner and Travd, originally devised to

explain the dissolution of metals in acid is introduced. This principle

states that when several electroactive couples are simultaneously present

at an electrode, the net current density of the mixture at a given

potential is the algebraic sum of the curves of each individual couple.

The catalytic situation is described in the particular case in which,

over a common potential domain, two electroactive couples show currents

of opposite polarity: in the absence of an external current source the

potential of the electrode adjusts itself to a value in that domain Em>

at which the two partial currents are equal and opposite in sign. Their

absolute value is the mixture current density, im. A catalytic

situation also requires the electrode material being inactive, save for

its role as a medium for electron transfer.

2

Spiro and Griffin have shown quantitatively that the reaction

between ferricyanide (also referred to as Feic, in this thesis) and

iodide ions proceeds through the electrochemical mechanism on platinum:

2Fe(CN) 6~ + 3I~ *2Fe(CN)e~ + U (1-1)

Spiro^ has produced an expression for the catalytic rate in the case

of two irreversible electrochemical couples, when E is in the Tafel m region of each couple, and also for the case in which it lies in the

limiting current region of one of them. These ideas have allowed

Miller et al.^ to account for the mechanism of the catalytic reduction

of water by a potential mediator in the presence of platinum, gold and

silver colloids. More recently, in the field of corrosion, a phenomenon 7 8

also subject to mixed potential control, Ritchie et al. ' have

independently developed expressions for the dependence of E^ on the

stirring of the solution in order to obtain diagnostic criteria for the

influence of mass transport limitations in the open circuit dissolution

of metal disks. There is therefore, considerable current interest in

the concepts of mixed potential and mixed current. Moreover, mixed

electrochemical processes, particularly on colloidal metal catalysts,

would appear to be more properly studied " in toto" , as it is not

always possible to study the individual couples separately. Therefore

the development of theoretical concepts and experimental techniques

for their study which allow their electrochemical nature to be pin-

pointed, would be most useful.

The main goal of this work has been to study the catalytic rate

of reaction (1) under a variety of experimental conditions and to

interpret the results in terms of the electrochemical model. In this

context, theoretical expressions for the catalytic rate have been

3

obtained to cover the eases of reversible couples and partial mass

transport control of irreversible couples. The catalytic work has

been complemented by electrochemical studies of the individual couples

concerned.

1.2. Thermodynamics of the Metal/Solution Interphase.

The che.ical po te n t i a l^ o f a spee.es, ,, insiae a Phase, „. is

defined as a a

m ( ' G , , V n ^ j ) , T , P , etc.

= y?^ + RT In a? (1-2) 3 3

a a a G is the Gibbs free energy, n_. are the numbers of moles of j, a. is a the activity and y_. is the value of y. at unit activity. Chemical

reactions are only possible if the chemical potential of the products 0!

is not equal to that of the reactants. y_. is a measure of the energetic

value of j in its chemical interactions with other species that dwell

in the phase. If the species bear an algebraic electronic charge, ZJ9 Of in a phase a with electrical potential, <J> , the extra electrostatic energy is —0! taken into account by introducing the electrochemical potential, y.,

9 devised by Guggenheim and defined as:

— fy ry Of y = yT + Z F<j> (1-3) J 3 j

When two phases are brought into contact, like a metal (M) and an

electrolyte solution (S), the condition of equilibrium is expressed as:

-S -M Ay. = y? - y. = 0 (1-4)

3 3 3

for each species, j, capable of crossing the interphase (e.g., j =

electron, for redox electrodes; j = metal ion, for metal-ion electrodes)

4

Eq. (3) effects an artificial separation between the " chemical" and 11 electrical" interactions that contribute to the free energy of a

Of substance; but it is a sound concept in the sense that it defines (}) 10a

unequivocally, and that no inconsistencies result from its use.

Moreover, cf>a coincides with the concept of electrostatic potential.

It is known as the inner (or Galvani) potential of the phase. It is

impossible to measure because no operation can be prescribed by which (X

a test charge brought from vacuum into the phase can test cf> only,

while not experiencing all the " chemical" influences of the phase.

The same argument applies to the absolute potential difference, A<j>, ct B between two phases ((j) -<j) ); also, the need to have a probe inside one

of them creates an additional interphase and an additional A(|) that enters 11a.

into the measurement. However, changes in A(f> can be measured,

provided that the potential difference generated by the probe does not 11a change upon imposition of a voltage,V , from an external power source.

In effect (Figure 1), according to Kirchhoff's first law!

A<j>i - Ac}) 2 + V = 0 (1-5)

Taking differentials and assuming that A(j>2 is independent of V, gives!

dA<J)x = -dV (1-6)

(It is assumed in eq. (6) that the S phase has a negligible ohmic

resistance; it is valid, however, if dV does not lead to a current flow.

This would not be true if the interphase is in contact with a redox

system, see below).

For a redox couple Ox/Red with charges Zox and Z^j , respectively

in contact with a metal electrode: k ox Ox + ne ^ Red (1-7) K J red

V

1 1 1 1 11

3 MI S M2

A<fe| M>2

Figure 1 - 1

F i g u r e

r e a c t i o n coordinate

1-2

6

At equilibrium use of eq. (3) yields:

-S -M ,-S -S . -M 0 = ny e- - ny e- = ( y ^ - ^ - ny £- (1-8)

Combining eqs. (2) and (3) for each species, and remembering that ^ • 12 Zox - n = o n e obtains : M S E = A* = $ - <f> = A(J)° + (RT/nF) In (a /a ,) (1-9) ox red

where E° = = -(y° , - y° - ny°-)/nF (1-10)

red ox e

Eq. (9) is the Nernst equation for the partial reaction (7) . Acj) and

A(f>° can be referred to a common arbitrary reference potential. For

redox systems at equlibrium the Nernst equation (9) is equivalent to

the equality of the electrochemical potentials. The inference follows

that if A(J) is made to depart from its Nernstian value, the electrons

in the metal will not be in equilibrium with the electrons in the

solution and a net flow of them will occur across the M/S interphase.

The non-equilibrium situation is outside the realm of thermodynamics.

1.3. The Butler-Volmer Equation,

a) Simple Electrode Reactions.

An expression for the rate of electron transfer across the metal/

solution interface when Acf> is made to depart from its Nernstian value 13 14 ^rev W a S by J«A.V. Butler and independently by IA. Volmer.

As a first approximation^^ the cathodic and anodic rate constants k ox and k ,, respectively [see eq. (7)J can be obtained from the absolute red

l i b reaction rate theory :

k = (kT/h) exp(- /RT) (I-lla) ox ox

kred = ( k T / h ) e x p (' ^ e d / R T ) (I-llb)

where k is the Boltzmannconstant, and h is the Planck constant. The net

7

current density is:

i = F k C - F k .C . (1-12) ox ox red red

Figure 2 shows the electrochemical free energy G of reactants and

products, measured from some arbitrary value. The only step in

consideration is the charge transfer; any other process like transport

of Ox and Red to the electrode or metal-ligand bond formation are S M

either absent or in equilibrium. A change in c|> -<j> will displace both

curves if both reactants and products are charged. The electrochemical

free energy of the species are: - M M M , -i o \ G = nG nF$ (I-13a) ne- e-

• < 4 + zo> f* s ( i - i 3 b )

5red = Gred + ( I" 1 3 c )

The displacement of the reactant curve relative to the displacement of

the product curve effected by the existence of <f> is:

M S S (-nF<j) + Z0XF(J> ) - ZredF(J) = -nFAcf> (1-14)

This is why in Figure 2 only the reactant curve has been displaced

upwards by an amount, -nFA<j> (meaning that A<j> has been made more negative)

From there it seems clear that at the crossing point of the curves this

contribution is only cmFA(f), with 0 < a < 1; a is known as the symmetry

factor. If AG^ is the activation energy in the hypothetical case when

A<f> = 0, then

AG^ = AG^ + anFA(j> (I-15a) ox o,ox

8

Introducing eqs. (15) in eqs. (11) and in (12):

I = FkC exp(-anf A<j>) - FkC , exp[ (1-a) fnA<J) ] ox red

where (kT/h) exp(-AG^ /RT) r o, ox

(kT/h) exp(-AG^ ,/RT) o, red

F/RT

(1-16)

(I-17a)

(I-17b)

Eq. (16) is known as the Butler-Volmer equation. When A<J> = Acf) then rev i = 0 since the backward and forward rates must be equal. Thus, we

can introduce the exchange current density, i0, by:

i0 = Fk C exp(-anf A<f> ) = FkC , exp[ (l-a)nfA<j> ] (I-18a) ox rev red rev

The standard exchange current density, ioo> is the value of i0 when all

the species are at unit activity:

ioo = Fk exp (-anf A<f>°) = Fk exp[ (l-a)nf A(j>° ] (I-18b)

Introducing eq. (18a) into (16):

i = i0 (exp(-ofnfn) - exp[ (l-a)nf n ]) (1-19)

where the overpotential n is defined as:

n = A(j> - Ac{) rev (1-20)

The shape of a steady state current-voltage curve according to

eq. (19) is shown as a broken line in Figure 3. The current grows

almost exponentially with n if |n|^_ca. 0.1/n V. In practice, as the

electron transfer becomes faster and faster, the slower mass transport

rate begins to hold up the current until it reaches a limiting value

(see section I.5.a).

9

b) Consideration of Pre-Equilibria-16a K.J. Vetter, has introduced the possibility of fast chemical

or electrochemical steps preceding a slow rate-determining step (r.d.s). 11c

The derivation given by Bockris and Reddy, will be followed here.

Suppose that reaction (7) goes through the following sequenceI

Ox + pe ^ vSr (I-21a)

v(Sr + pe" » Sr+1) (I-21b)

vSr+1 + pe » Red (I-21c)

where S^ and are intermediate species. Reaction 21b is the r.d.s.

which occurs v times when the overall reaction (7) occurs once, v is

the stoichiometric number of the reaction. During the r.d.s. p electrons

are transferred at once. Reactions (21a) and (21c) are assumed to be

so fast that they are effectively in equilibrium at the electrode

potential Acf). They can occur through a sequence of steps in which

electrons may or may not be transferred (each step being also at equili-

brium) . From eq. (7) and from the sequence (21) it follows that:

p + p + vp = n (1-22)

Applying eq. (16) to the r.d.s. in (21)!

i = F k r d s c r exp(-crpfA<f>) - F \ d scr + 1 exp[ (l-a)pf A<|> ] (1-23)

Since (21a) is in equilibrium during the forward reaction and (21c)

during the backward reaction, the Nernst equation may be applied to

each of them to obtain the concentration of the intermediates S and

10

Therefore:

where

Cr = K 1 / V C ^ V exp[-(p/v)fA<|>]

Cr+1 = ( Cied 7^ 1 / V ) exp[(p7v)fA<{,]

K = exp(p f A<j>°) , and K = exp(p f Acf>°)

(I-24a)

(I-24b)

(1-25)

Introducing eqs. (24) into (23)1

where

t - t . K 1 / V , and k - t . / K 1 / V

rds ' rds

(1 -26)

(1-27)

By analogy with eq. (16) the anodic and cathodic transfer coefficients

a and a, respectively, are defined as:

and

~ct = ap + , and a" = (n-^)/v - ap

a + a" = n/v

(1-28)

(1-29)

Use has been made of eq. (22) to obtain a. Similarly to eqs. (18) the

exchange current density, and the standard exchange current density are!

io = Fk C 1 / V exp(-afA<|) ) = Fk C 1 ^ exp(afA6 .) (1-30) ox r Trev red Yrev

i00 = Fk exp(-afA<j)°) = Fk exp(afA(f>°)

Substitution of eq. (30) in (26), and using eq. (20)'.

(1-31)

i = i©[exp(-afn) - exp(offn) ] (1-32)

11

This is the more general form of the Butler-Volmer equation, when

all the steps other than the r.d.s. are in equilibrium, in the absence

of mass transport limitations and of adsorption of reactants or inter-

mediates at the electrode surface. Since in principle any number of

substances can enter in the pre-equilibria, several Cj can appear in

eq. (26) , not just C q x and Their exponents will vary too and

will not necessarily be 1/v, but any number, W.

c) The Tafel Approximation.

If ri is sufficiently negative, the second exponential term in

eq. (32) can be ignored with respect to the first. Thus, in logarithmic

form eq. (32) assumes the form known as the Tafel equation:

2.303 . . 2.303 , . .. ^ n ,r oo N n = — ^ — log i0 ^ — log i, if n « o (I-33a)

n = - 2 , 3 0 3 logio + 2 , 3 0 3 log (-i) , if n » 0 (I-33b) af "af

The usefulness of the Tafel equations is obvious since plots of

n vs. log|i| are linear; the slope yields ~a or "a, depending on which

region of ri is being considered, and the intercept provides the exchange

current density. As a rule of thumb, the Tafel region should occur if

|n | > 0.1 V for one electron reactions, or if | r\ | > 0.05 V for a two-

electron reaction. If the reaction does not strictly follow eq. (32),

i.e., in the presence of " complications" , this is more likely to be

detected in the Tafel plots in the form of curvatures, of disagreement

between the anodic and cathodic i0 values, or in failure of a + a to

comply with eq. (29).

12

d) Approximation at Low Overpotentials.

For small values of n one can expand the exponential terms in eq.

(32) in series. If the terms in n of order higher than one are ignored:

i = i0[l - afn - (1 + afn)] = -(n/v)i0fri (1-34)

Apart from some obvious utilitarian aspects, eq. (34) offers a glimpse

of the intimate workings of the electron transfer in the context of the

absolute reaction rate theory. Thus, for example, a small departure

from Ad) causes a linear increase in the number of reactant particles Trev r

capable of producing an activated complex, hence a linear increase in i.

It is also seen that the more often the r.d.s. has to be performed, the

lower the current is (other factors being equal), because the n electrons

have to be milled v times in succession through the slow r.d.s. Another

aspect is the absence of any symmetry factors, which are related to the

relative slope of the energy profiles in Figure 2 at the intersection

point. At equilibrium, the activated complex crosses the top of the

activation barrier with the same frequency in both directions; therefore

the actual slopes of the free energy curves have no importance. For

small departures from equilibrium one would expect this obliviousness

w.r.t. the slopes to be preserved, because the forward and backward

frequencies are still essentially the same.

1.4. Electrochemical Reaction Orders and Activation Energies.

The electrochemical reaction orders, W , were first introduced by

K.J. Vetter.^k By analogy with ordinary chemical reactions:

wj = (Bin i/31n C .)T, P, A<j>,Cfe(k j) (1-35)

13

The condition of constant Acf) is due to the potential dependence of

i. According to eq. (35) the W. are the exponents of the concentrations

in the pre-exponential terms of eqs. like (26). It follows that they

should be measured in the Tafel region, otherwise they become A<J>-

dependent. The superscript T stands for " an" or " cath" , depending

on whether the anodic or cathodic Tafel regions are being considered.

Another definition of W. is*. J

W' = Oln i/91n C.)_ , . (1-36) 3 3 T,P,n,Ck(kfj)

These Wj are the reaction orders of the exchange current density [see eqs.

(32) and (30)], and since n = const., the W_! contain the concentration

dependence of Ac}) . Unlike w T , Wj can be measured at any r\ value,

provided that it is constant, and Wj will not depend on ri or on A<f>. T The relation between W_. and W_! is, from consideration of eq. (30):

W! = Wan + * v. or W = W C a t h- ^ v. (1-37) 3 3 n j 3 3 n j

The value of the W! do not depend on which Tafel region is being used.

Vj is the stoichiometric coefficient of j in the overall reaction (positive T

for oxidants, negative for reductants) . The W^ have a direct kinetic

value in the sense that they appear in the kinetic laws as a direct

consequence of the operating mechanism, while the Wj may be seen as a

consequence of mathematical handling of equations like (26). ¥ 17a The electrochemical activation energy E is defined as I

E*. = - R[91n k /3(1/T)]_ _ .. (I-38a) ox ox C',r,A(|) J

4 d " - R [ 3 l n kred/3(1/T> ]C, ,P,A* ( I" 3 8 b ) J

Using eqs. (11) and (15)'.

4 4 E = RT + AG + anFA({) (I-39a) ox o,ox

14

E^ , = RT + AG^ j - (1-a) FA<J> (I-39b) red o,red

Setting E^ = E^ when A<b = A<> : rev rev

E^ = E^ 4- anFri (I-40a) ox ox,rev

E^ - = E^ j - (l-o)nFn (I-40b) red red,rev

Because varies with temperature, correction must be made to eqs.

(40) for the temperature coefficient of A<|> . As expected, E^ rev

decreases for the cathodic reaction if TI is made negative; the same

happens to the anodic reaction if n is made positive.

1.5. Corrections to the Butler-Volmer Equation,

a) Effect of Mass Transport Limitations.

When the rate at which the reactants can reach the electrode or at

which the products can leave it is not fast compared with the electron

transfer itself, these steps must be introduced in the reaction scheme

and their rate allowed for. Therefore, reaction (7) which occurs through

a sequence like (21) must be described as:

_ convection/ _ /i \ (bulk) diffusion 3 °X(0HP) ( I" 4 1 a )

°X(0HP) + n e" ^ R e d(0HP) ( I" 4 1 b )

Red convection/ (l-41c) (OHP) diffusion Ke<3(bulk) U

In this sequence " bulk" means that the chemical is positioned just

outside the diffusion layer at which its concentration equals C , i.e.,

its bulk concentration. It is assumed that the electron transfer proceeds

15

when j is at the outer Helmholtz plane (see section I.5.c) at which

its concentration is C^. It is assumed that none of the major steps

in (41a-c) is in equilibrium. Step (41b), however, is still described

by the sequence (21). In the steady state the rate of each step is the

same. Therefore:

Rate of (41a) = i = nFD (C - C° )/6 (I-42a) ox ox ox ox

Rate of (41c) = i = -nFD ,(C ,)/5 , (I-42b) red red red red

The rate of (41b) is also i, given by eq. (26), except that C must be used,

Sdlving for C in eq. (42) and introducing them into eq. (26) and

using eq. (30) TTcath TT an w w ox / r. \ . /, \ red i = i0[(1-i/L ) ° X exp(-afn) - (1-i/L ,) r e d exp(afn) ] ox red (1-43)

The L_. are the limiting current densities, defined by'.

L = nFD C /6 , L , = -nFD ,C ,/S , (1-44) ox ox ox ox red red red red

Eq. (43) will yield curved Tafel plots in the |n| > O.l/n region. If

V/Cath (or W a n ,) = 1, then at constant n: ox red '

1/i = 1/Lqx + 1/i ., i^ = i0 exp(-afn) (1-45)

L^^ can be controlled by varying the stirring of the solution (see

Chapter II), and a plot of 1/i vs. 1/LQX yields i^ at infinite stirring.

With several plots at different n each, a mass transport-free Tafel plot cath an

is obtained from r) VS. log i^. If W q x (or W^^ 1, the corresponding

plot, at constant n is: In i = W C a t h In (1-i/L ) + In i. (1-46)

O X O X K

t cath from which i. as well as W can be obtained, k o x

16

A different situation occurs when all the electron transfer

steps in (41) are much faster than mass transport [therefore (41b)

can no longer be represented by (21) ] and the Butler-Volmer equation

cannot be used. In the steady state, the rate of (7) is that of the

slow steps (41a) and (41c), given by eqs. (42), while (41b) is in

equilibrium at the electrode potential Acj>. Thus, with reference

to reaction (7);

Acf> = AcJ)° + ln(C /C ,) nf ox red'

= AcJ> + rln[ (1-i/L ) / (1-i/L ,) ] rev nf ox red (1-47)

where A<f> is given by the Nernst equation. According to eq. (20) I

= "V ln[(1-i/L )/(1-i/L ,)] nf ox red (1-48)

r) is called the diffusion or concentration overpotential, 16c and the

couple Ox/Red is termed " reversible" . In this situation no kinetic

information can be gained from the study of i-A<|> curves. Or, put in a

positive way, no such knowledge is required to describe reversible

electrochemical systems.

b) Migration of Ions.

Charged reactants and/or products can also reach the electrode by

migrating in the electric field between the electrodes. Migrational

effects hinder the reduction of anions and assist their oxidation and

vice versa for cations. Because a travelling ion in solution contributes

to the current being passed, the fraction of the current carried by the 16d ion is represented by its ionic transfe r ence number t :

t. = J Z. u.c. j .1 .1

? l z k l v

, and E t, = 1 k k

(1-49)

17

where u_. is the ionic mobility of ion j. The summation takes into

account all of the other species in the solution. If j is the species

whose electrode kinetics are under scrutiny, then the complicating

effect of its electrical migration can be effectively avoided by

adding a large excess of supporting electrolyte. This is a salt that

does not undergo electron transfer in the same potential range as does

j, but being dissociated into ions and present in large amounts

compared to j, it is capable of carrying most of the current through

the solution. According to the example of hydrogen evolution from

H2S0z,/Na2S0/, solutions cited by Vetter,"^6 migration effects on the H +

ion are almost completely eliminated for [Na2S0A ]/[H2SOz, ] ratios as

low as unity. It seems reasonable to assume that the same order of

magnitude for the ratio [sup. electrolyte]/C^ should apply generally.

However, there are other reasons for preferring ratios 2 and 3 orders

of magnitude higher as it is always done in practice, in order to

maximise the conductivity of the solution (see Chapter IV) and to

minimise double layer effects (see next section). It also keeps

activity coefficients constant, which affect formal electrode potentials

c) Double Layer Effects.

The consideration of double layer effects was originally made by 18

Frumkin. The situation is sketched in Figure 4, where the metal/

solution potential difference A<j> has been broken down into several

sections corresponding to the various layers of ions.

It is assumed that the electron transfer takes place when the reacting

ion is positioned in the OHP. Two results follow. The first, apparent

from the figure, is that the acting potential difference is not A<j), but

only A<j)-A<j> . The second is that the electric field in the diffuse

18

t r a n s p o r t - free j /

/ / ,

/ / t r a n s p o r t - influenced /

overpotential

Figure 1 - 3

distance f r o m electrode

Figure 1 - 4

19

double layer imparts to the charged species, Ox, an extra energy

(compared to the bulk of the solution) which makes its concentration

at the OHP depart from the bulk value. Thus, according to the

Boltzmanndistribution law:

OHP Cunr = C exp(-Z fA(b _) (1-50) ox ox ox OHP

Eq. (16) must be modified accordingly to contain only the relevant

A<j> s and C s. Therefore (for the cathodic reaction only):

i = FkCox exp(-ZoxfA(f>0Hp) .exp[-cmf (Acf,-Ac|)0Hp) ] (1-51)

rev j At the reversible potential, Act = A<J> , because A<J> depends on Ac}), U n r Urir (JHr

Thus, ^ r p t r ,y v» p y

K = exp(-ZoxfA^0HP > exp[-anf (A^ev-A4,0Hp ) ] (1-52)

Introducing (52) into (51);

i = iQ exp[(^-Zox)f(A<})0Hp-A(t)^p )] exp(-ahfn) (1-53)

where i is given by eq. (18) . Generally Acf> depends on Ac}) through O (Jrir

complicated expressions involving the capacitance of the diffuse and

compact double layers, as well as the dependence of the contact-adsorbed

charge with the charge on the metal. In treatments like this, the

validity of applying the equilibrium concepts used in double layer theory

to the non-equilibrium process of charge transfer must be considered.

Double layer effects are likely to arise in dilute electrolyte solutions

where the diffuse layer is well developed, but in concentrated supporting

electrolyte, the diffuse layer is almost completely squeezed against

the OHP, which reduces the double layer effects. Even in those solutions,

however, if the reacting ion is large, e.g., ferricyanide, this creates

a new plane further into the solution than the OHP of the supporting

electrolyte. This introduces the need for certain corrections, which

may, however, be difficult to evaluate numerically.

2 0

d) Adsorption.

Adsorption on the electrode is an important and widespread

phenomenon. general situations may be considered: adsorption

of participants or intermediates in electrochemical reactions, and

adsorption of foreign (often organic) electroinactive substances

which may affect the kinetics of electrode reactions. In the former

case, it is difficult to introduce adsorption in a general scheme

like eqs. (21) since adsorbed intermediates may react to give new

adsorbed sustancesj simultaneous discharge from species in the solution

and combination with adsorbates may occur too. Strong adsorption of

a reactant may speed the electron transfer step because closer contact

with the electrode must greatly increase the probability of electron

tunnelling, but too strong an adsorption of the product may block the

electrode, thus decreasing the rate of the reaction. Where adsorption

is present, the reaction usually presents more than average sensitivity

to the structure of the electrode surface. A brief account will be given

of the kind of mathematical modelling normally u s e d . ^ ^ L e t u s assume

that reaction (7) proceeds through the following sequence!

°X(bulk) + e" Red(S) ( I _ 5 4 a )

Red(S) ^ Red(bulk) (I"54b)

^here the subscript S means an adsorbed chemical. If the desorption

step is rate-determining the current is given by:

i = fkG (1-55)

where 0 is the degree of coverage by Red. If (54a) is very fast, then

by the assumption of equilibrium the forward and backward electronation

rates must be equal:

21

Fk(l-6)Cox exp(-af AcjO = Fk6 exp[ (1-a) f A<|> ] (1-56)

The term (1-0 ) arises because Ox can only discharge on the part of

the surface not yet covered by Red. From eq. (56) the Frumkin

adsorption isotherm is obtained:

0/(1-6) = K C exp(-fA<f>) (1-57) OX

where the adsorption equilibrium constant K is given by:

K = k/k = K exp(-g0/RT) (1-58) o

Here K has been expressed under the Temkin condition of linear increase

in the standard free energy of adsorption with coverage. The parameter,

g, is related to lateral interactions between the adsorbed Red molecules,

If the molecules attract each other laterally in the monolayer, then

K increases with 0. This would be reflected in a negative g. In the

opposite case, lateral repulsions., K must decrease with 0 to reduce

the " loathed" crowding at high coverage and g is positive. The

Langmuir isotherm is obtained for g = 0 at constant potential.

Introducing (57) into (55):

kK C q x exp(-fA$) 1 = 1 + KC exp (-f A<j>) (I~59)

ox

The Tafel plots will thus fail to produce straight lines. If the

electron transfer step is the slow one, 0 is bound to be small and

independent of A<p, and its effects on the kinetics will be small too.

e) The Transfer Coefficient, a.

According to Figure 2, the transfer coefficient represents the

fraction of the applied electrical free energy that is used to change

the height of the activation barrier. Or:

2 2

a = [ 3AG^/3 (nFA<j>) J (1-60)

a must have a value between zero and one. The actual value is

determined by the relative slopes of the free energy curves at the

intersection point. If reactants and products are chemically very

similar their curves will be also of similar shape and slopes. Under lie

these conditions a fy 0.5 and will be nearly independent of A<j>.

The latter indicates that the intersection occurs high in the branches

of the curves where the slopes change less drastically. Thus, for

high activation reactions (slow reactions), a is nearly constant, while

it changes with A<f> for fast reactions which show a low activation

energy so that the intersection takes place in the lower part of the

curves. The exact dependence of a on A<|) depends on the theoretical treatment used to describe the free energy curves. Modern electron

15 19 20

transfer theories ' ' emphasise the rdle of the solvation sheath

around the ion in bringing the electron energy levels of the reactant

to an intermediate stage at which an electron in the metal with the

same energy can tunnel through the double layer to the ion. The theory

at present only applies to reactions not involving breaking or forming

of chemical bonds or strong changes in metal-ligand interactions during

the electron transfer. Verification of the theory is being currently

attempted in two main lines of research: correlation between rate

constants for homogeneous electron transfer reactions and heterogeneous 21 electrochemical rate constants, and in the measurement of a as a 22

function of potential. Although changes in a have been measured, the

cause of their variation is not undisputed, double layer effects being

the most serious correction that need to be applied. In any case, these

changes are small and within the experimental uncertainties in the

ordinary conditions of most electrochemical work, other reasons for

changes in the slopes of the Tafel plots being more important.

23

CHAPTER TWO

THE HETEROGENEOUS CATALYSIS OF REDOX REACTIONS

II.1. Introduction. 3

Figure 1 illustrates the addivity principle of Wagner and Traud,

as explained in Section 1.1. The same figure may serve to illustrate

either the dissolution of a metal in acid or the reaction between an

oxidant and a reductant in the presence of an inert electrode. In

both cases the net transformationI

v 0x2 + v , ^edi > v <red2 + v Oxi (H-l) ox^ red4 recla Ox,

is decomposed into two partial reactions of concerted occurrence!

v Ox2 + e >v , t*ed2 (II-2a) r e djt

v « i edx > v oxi + e (II-2b) rea^ o*^

(It is convenient to represent these as one electron reactions which

means that the stoichiometric coefficients v! have been divided by n.J J J thus Vi = vj/ni, and v2 = v2/n2). The resultant i-E curve is displayed

as a broken line in Figure 1. The salient feature of this type of

chemical process is that at E =E m , although the net current is zero,

a net chemical change is occurring, which does not necessarily require

physical adsorption of the reactants onto the catalyst. It was a major

advance to have realised that the dissolution process corresponds to

that single point in the net curve. The extension of the principle to 2

the catalysis of redox reactions by Spiro seems a natural one, and a

useful one too because it places the phenomenon in the context of hetero-

24

a CD

Figure 11-1

red,-> oye~

,rev

a QJ

o x + e " — > r e d ' 2 2

.rev

Figure 11—2

25

geneous catalysis where it can be used by researchers who are not

necessarily acquainted with electrode kinetics. Of course, when two

electroactive species are present at an electrode and specially if both

became adsorbed, interactions other than electron transfer through the

metal are conceivable, like direct electron transfer between adsorbed

species or the appearance of new reaction paths. A 100% electro-

chemical mechanism cannot therefore be taken for granted.

Spiro and Ravno"*" have pointed out qualitative conditions in which

catalysis by the electrochemical mechanism could be expected. With

reference to Figure 1 a large positive difference E2-Ei would cause

the curves to intercept at higher current values. The effect is enhanced

if the reactant/product ratio is kept as high as possible. In the case

of a highly irreversible couple ox'"/red'" which possesses a small i0 value

the mixture current is small and so is the catalytic rate. A survey" "

of over 80 solution reactions in the presence of platinum bear out this

theory. 3

In their original paper Wagner and Traud pointed out some

experimental procedures that proved helpful in their study of zinc amalgam

dissolution in acid, and the reduction by H2 of oxygen, K2S208, H3AsO/»

and nitrophenol in the presence of platinised platinum.

a) The slope of the net polarisation curve is measured in the neighbour-rev hood of E^. If one of the couples is very reversible (say E^ fy Ex )

the mixture current is calculated according to the expression:

The calculated value can then be compared with the experimental rate

of dissolution of the metal, or of consumption of a reatant dN/dt (in

moles per unit time), according to

E=E (II-3)

m

dN/dt = i /nF m (II-4)

26

rev If E does not fall too close to any of the E. the Tafel or the m J

Butler-Volmer equations are used to derive a relation between dN/dt

and ( 3 i / 3 E ) A s s u m i n g first order dependence on reactants and

products, the final expression is:

dN/dt - i | | /[«i + a2 + Bi/tt-Bi) + 1 / 0 " B a ) ] (II-5) ' E=Em

where

B^ = exp[-(c^ + o\)fn J (II-6)

The subscript j refers to the couple ox^/red^ ; TI is defined according

to eq. (1-20) for each couple.

b) The potential of the mixed system can be forced (e.g., potentio-rev rev

statically, or galvanostatically) to acquire the value Ei or E2 in

which case the transformation rate for the couple concerned should

cease, if only the electrochemical mechanism is operating.

The advantage of these methods is that the electrochemical measure-

ments are performed at the mixed electrode, except in cases where eq. (5)

is applied because some assumptions have to be made about the value of

the a values in the mixed system. In the second method, if the

reversible potential being enforced happens to lie in the limiting current

density region of the other couple, then any non-electrochemical surface

reaction will disappear, as C^ = 0 for the species under limiting

current situation, thus giving the impression that the electrochemical mechanism is being followed. It is conceivable in the catalytic situation

rev

that the E might fall in a region where the catalyst ceases to be

electrochemically inert, creating the possibility of more reactions

between the components of the system. More generally, it could be said

that since the concentrations of reactants and products are changing rev during the reaction, so do the values of E and E.

m j

27

An alternative experimental approach used by Spiro and Griffin

is that of obtaining the separate steady state i-E curves of each

couple, and compa ring the resulting i^ and E^ with the experimental

catalytic rate u and with the catalyst potential E at zero time, cat cat The same electrode surface, treated in identical ways, must be used in

both sets of experiments. This approach gave surprisingly good results

in the case of reaction (1-1) catalysed by platinum. It constitutes

the basis of the theoretical treatment in the following sections in

which expressions for i are obtained under several experimental

conditions.

II.2. Quantitative Model of the Catalytic Rate.

a) Assumptions.

The catalytic rate v is the value of the overall rate.v , .less J cat ' obs' the value of the rate v, in the absence of the catalyst! hom

V , = V + v, (II-7) obs cat hom

It will be assumed that v ^ and v, are independent of each other cat hom (but see Appendix 1) . The relation between v (in mol € min "S and

Car

the specific catalytic rate ufaj.(in m°l P e r unit area per unit time) is

vcat = Aucat' V (II"8>

and u . = i /F , v = Ai /FV (II-9) cat m cat m

It will also be assumed that the whole of the catalyst surface area is

available to the reactants. Therefore, it is immaterial to refer to

current densities, i , or to net currents, i will be used all the m m

time, but it will be made clear when net current is being referred to.

The mixture current is given by the sum of the currents of the individual

isolated couples. Positive sign will be given to both anodic and

28

cathodic currents. The catalyst is taken to be in the form of a

rotating disk at which the Levich equation for the limiting current 23 density applies :

-3- _ JL _L (11-10)

2_ _ JL_ L. = 0.620 nF D.3 v 6 oo2 C. 3 3 3

where n represents the number of electrons transferred, D. is the 3

diffusion coefficient, v is the kinematic viscosity of the solvent

(= viscosity divided by the density), w is the angular velocity of

the disk, and C is the bulk concentration of the species undergoing

electron transfer. The mass transport rate constant k_. and the parameter, o. are defined by!

3

L. = k.C. (11-11) 3 3 3

L. = a.u)2 C. (11-12) 3 3 3 It follows from eq. (10) that

_2 1 _1_ k. = 0.620 nFD.3 v 6 a)2 (11-13) 3 3

and a. = 0.620 nFD.3 v~ 6 (11-14) 3 3

b) Case of Two Irreversible Couples.

This case has been considered by Spiro,"* assuming that E lies in m the Tafel region of each couple. If subscript 1 stands for the couple

that undergoes a net oxidation and 2 for the one that undergoes a net

reduction:

rev ix = ioi exp[(l-a1)Z1f(E-E1 )] (II-15a)

rev i2 = ioa exp[-a2Z2f(E-E2 )] (II-15b)

where Z.is the number of electrons divided by the stoichiometric number 3 and a_. is the transfer coefficient of each couple. At the mixture potential,

29

E = E , ii = i2 = i (11-16) m m

The expression for i obtained^ was: m

an TJcath i = iooi ioo2 exp[a 2Z 2r 1f(Ej -E® ) ] ( n c 5

2 ji) C H c Y 2 j 2 )

j. 3 1 4 J 2 m

(II-17)

= (l-a1)Z1 = a2Z2 / J J _ I o \ 1 (1-ax) Zi + a2Z2 ' (l-ai)Zx + a2Z2 ^

iooj are the standard exchange current densities, and the wl are the

electrochemical reaction orders. Eq. (17) shows that the catalytic

rate will be larger the larger E2-E° and the larger iooj» Another

feature is that since the r_. are in general fractional numbers, it

follows that the reaction orders will not be in general whole numbers.

Spiro has pointed out that this behaviour may give the superficial

impression that reaction (1) proceeds through a L angmuir-Hinshelwood

mechanism with ox.2 and redx adsorbed by Freundlich isotherms, the r.d.s.

being the interaction between neighbouring adsorbed species.

b) Partial Control by Mass Transport to the Catalyst.

Using relations previously mentioned (Section I.5.a.), and assuming

that only one reactant species*is affected by mass transport, the following

equations are obtained in the Tafel region: W

i = (1-i /L , ) r e d l ioi exp[(1-ax)Zxf(E -EieV)] (II-19a) m m redx m W

i = (1-i /Lox ) 0 X 2 i02 exp [-a2Z2f(Em-E2eV)] (II-19b) m m - 2

(Thus, it is not necessary to specify the Tafel region in which the W s

are being considered).

* of C0tf|>l£

3 0

In logarithmic form!

rgTT In i = In ioi + W , ln(l-i /L , ) + (l-ai)Zxf(E -Ei ) (II-20a) m redi m redi m VpTT In i = In ioi + WnY ln(l-i /Lnv ) - a2Z2f(E -Ea )

m ox m 'ox m (II-20b)

To eliminate E^, multiply eq. (20a) by a2Z2 and eq. (20b) by (l-ai)Zi,

add them and divide by (l-ai)Zi + a2Z2 throughout! r 2W , r iW0x

In i = In(ioi ioi) + ln[(1-i /L ) redl(l-i /L0* ) 2] + m m redi m *2

+ r i a 2 Z 2 ( E le V - E ^ e V ) (11-21)

Now, if a)—> then L. > 00 and i » i . Therefore: j m m,°°

In im = In (i01 x02J + ria2Z2 (E2 - Ex ) rev „rev, (11-22)

i is given by Spiro's eq. (17). Eq. (22) is an equivalent expression. m

Introducing eq. (22) into (21), rearranging and eliminating the logarithms:

r 2 W m m,00

1-m

Jredi

red: riW, ox 1 - m

J0X

(11-23)

The binomial expansion can be applied to the bracketted terms. If

i « L. only the first order terms in i /L. need be considered. Thus: m 3 m j

(11-24)

Eq. (24) allows the determination of the rate of the surface reaction

by extrapolating plots of 1/u vs. l/oo2 to infinite rotation speed. car

31

Still under the assumption i /L. « 1! m J

ln(l-i /L.) % -i /L. - (11-25) m j m j

If eq. (25) is used in eqs. (20), and if (20b) is subtracted from (20a)

to eliminate In i , then E can be solved for: m m

(11-26)

where

(II-27)

According to eq. (26) the catalyst potential should vary linearly with

the ratio u /w2, if the electrochemical mechanism is operating. The cat sign of the slope should be governed by the chosen experimental system.

It is possible to obtain an explicit dependence of E on co by introducing m expression (24) into (26) but the resulting equation is not easy to use

in practice. However, solving for the ratio im/w2 in (24) and

introducing it into eq. (26) gives

„ „rev „rev E m oo = + r 2 E 2 +

Of 2^ lo 1

E = E + (a/b)(1-i /i ) (11-28) m m,00 m m,°°

where a is the slope in eq. (26) and b the slope in eq. (24). Thus, a

linear relationship between E and \J as u is changed is predicted Cat Cat

for the electrochemical model. Since eq. (28) is a relation between E m

and i it seems that compliance with it would provide important evidence m in favour of the electrochemical mechanism, if the system satisfies all

the assumptions made.

32

Comments.

Equations similar to (2V) are bound to appear also for any non-

electrochemical mechanism subject to partial mass transport control.

But the slope depends on the mechanism, and in the case of mixed

potential control it could be compared with the slope calculated from

the electrochemical kinetics of each couple. It is most useful to

determine the value of the surface reaction rate u under different cat,00

conditions.

It is very unlikely that E would follow eqs. (26) or (28) in the m case of a non-electrochemical mechanism, and compliance with either

of these equations would be strong evidence in favour of the mechanism.

Preliminary experimental tests should be made to check whether the

assumptions of the model are correct. The limiting current densities

of all the species should be compared with IJcat» i.e., the ratio

FU ,/L. calculated to see whether the binomial expansion admits cat j truncation after the second term. E should lie in the Tafel region

CH U

when the individual i-E curves are obtained. However, since the reactions

are usually carried out without the products being initially present, rev rev then Ei >-oo and E2

00 at zero time. Thus, as least in

theory it is always true that a Tafel approximation can be used, since

only the initial catalytic rate is being measured (because the slopes of

the concentration vs. time plots are always extrapolated to zero time).

c) Reversible Couples.

In this case the rate of diffusion across the diffusion layer is so

slow compared with the kinetics of electron transfer, that the latter

reactions are in equilibrium at the mixture potential (see Section I.5.a.).

Thus, applying the Nernst equation to reaction (2):

33

E = E° + (1/f) ln[(cii)V°,C-l/(C®edi)Vredl]

E = E°2 + (1/f) l n [ ( c ° „ y ° * v c l e d y e d > ]

(II-29a)

(II-29b)

where E is the electrode potential. At the mixture potential E = E , m i = i . Solving for the C°. in eqs(l-4<2.) and remembering that all the m J currents are positive!

E = E? + \ In m f (1 + i /L0X ) m i

ox ox J0x

( 1 - i / L , ) V r e d' C / 6 d l m redi redi

(II-30a)

E = E2 + j In m r (1 - i /L0 ) m K ?

"0X 'OX

'ox

(i + i /L , ) V d 2 c / r e d 2

m red2 red2 (II-30b)

Multiplying by f, re-arranging and taking exponentials:

ox redi ox 'redi

'<?x red: ox 'red:

K exp[f(E2 - E?)] = £ = h(i ) m (II-31)

where K is the equilibrium constant and Q is the reaction quotient

The function h(i ) equals m

= m (1 + i_/Lox ) V ' (1 + i /L_ _ j ) V d 2

m m red2'

(1 - i_/LOJt (1 - i_/L_ _,, ) V r e d l m m redi'

(11-32)

If the measurement of u ^ is constrained to the initial rate, C„v and cat ' ox x C j will both be very small. Then! red 2 3

i / Ln* » 1» a n d i /I j » 1 m m red 2 (11-33)

34

Furthermore, let us assume that for the reactants 0 x 2 and redi,

V ^ e d i ~ a n d W a « 1 ( " - 3 4 )

Introducing (33) and (34) into (32)

h ( i J * aJLo« ) V° y i ^JK.A ) V r e d 2 ( X I - 3 5 > m m c>x x m red 2

Solving for i , taking (31) and (11) into account m

(II-36a)

where <j> = l/(vQX + v j ) red;

A less severe approximation is obtained if the denominator of h(i ) ism binomially expanded, neglecting all terms in o p order larger than

unity. The resulting expression for i isI

1/i. = l/W + •(.„„ /L,, m + V J / L a > 2 redi redi (II-36b)

where W is the expression for i in eq. (36a). m

Because of the definition of k. in eq. (11), it follows that the net

order in oo2 is unity.

1 = m

j. v*. , v j v , , v^ <f> ox, <f> red2 «(> <|> redi r<J> ox.. O U j. JS. \j . 0x1 red2 redi ©x 2 (H-37)

35

Therefore, a plot of i vs. o)2 will be a straight line passing through m

the origin. The slope contains only transport and equilibrium parameters,

so that the same expression could have been obtained if one had started

from the equilibrium equation for reaction (1), regardless of the

nature of the mechanism. In this case one must prove that the only

equilibrium in existence is the electrochemical one, for example by

obatining the i-E curves of the separate couples and showing that within

experimental error u cat % ±m/F , and % E_. The effect of stirring m cat m on E^ should be tested too. In effect, according to eqs. (30) because

im and L_. are both directly proportional to o)2 , Em should be independent

of 03, other conditions being kept constant. The dependence of Em on the

concentration of the reactants can be tested too, although the analysis

as given here may be under conditions that are too restrictive. Assuming

eqs. (33), and also assuming that

i /L „ 0, and i /L % 0 m redi m ox*. (11-38)

then one obtains from eq. (30a)!

^ox, E £ E$ + ^ lnl m f rediJ

(11-39)

Introducing the expression for i in eq. (36) m

m (11-40)

Therefore,

O E /3 In C ) % (cj) v- -1)v , /f m redi C redi

( 8 V l n W c , * • v « > , / f

redi 1 2

(II-41a)

(II-41b)

36

24 Such an approach allowed Spiro et al. to show that reaction

(1-1) came to a rapid equilibrium on platinum electrodes, which suggested

that the mechanism involved electron transfer through the metal. [The

same result can be obtained starting with, e.g., (30b). However, in

practice one must choose the equation that is more likely to satisfy

condition (38), i.e., that in which the more concentrated reactant

appears].

It is possible to obtain an explicit expression for E . Assuming m eqs. (33) and (34), and multiplying eq. (30a) by l/vDX and (30b) by

l/vre(j , adding them and multiplying by vQJ< vr e d throughout:

E = <Kv j E? + v E 2) + C<f> \L /£) In CftSr - (<f>v J v , /f)ln C , + m red2 i 0* i 0 X 2 redi red2 redi

+ V 1 V d 2/ f ) l n ( k r e d 2

/ k o x i ) + v o X l W f ) l n ( 1 " V L O X 2 > "

- (<f> v , v , /f)ln(l - i /L , ) (11-42) redi red2 m redi

The situation described so far is valid only as long as the concen-

tration of the products is kept low during the reaction. The kinetic

law will now be analysed for high product concentrations.

Case II Consider first the addition of large amounts of the product

red2, while oxx is kept low. The rate will be very much depressed so

that:

i /L , « 1, and i /Lftsr « 1 (11-43) m redi m 0X2 also

i /L , « 1 (11-44) m red2

37

Since the other product is not initially present:

i / L m » 1 m i ( 1 1 - 4 5 )

Therefore, h(i ), eq. (32) becomes m v. r\. OX , h(i ) S (i /L ) 1

m m i (11-46)

Introducing eq. (46) into (31), and solving for i : m

i = k m OX OX

\) V I V , ox 2 redi c - red2 2 redi red2

1/v ox 1 exp[f(Ej-E?)/v ]

(11-47)

Case 2! Consider now a large addition of oxi while red2 is kept low.

Eq. (43) still holds ,but now

i « 1, while i /L , » 1 m i m red • (11-48)

Therefore!

w \ ^ /t \ red 2 h(i ) ^ (l /L ) m m red2 (11-49)

Therefore!

i = k , m red 2 "OX

c_ - C 2 „ Vredx "V0x redi ox

1/v red. exp[F(E2-E?)/V ] red 2

(11-50)

Case 3: Both products ox i and red2 are added in large quantities, but

the concentration of one of them at least does not exceed the final

equilibrium value in the bulk of the solution. Therefore:

i /L. « 1 m 3 (II-51)

38

for all i. Thus, h(i ) can be expanded binomially, neglecting all m terms of order larger than one in i /L., to yield m J

h(i ) £ 1 + i /L0 m m (H-52)

where

i/Lo = + /Lflk + v , / L , + v , / L . (H-53) ox x x ox 2 2 redi redi red2 red2

Solving for i in eq. (31) gives m

(11-54)

Comments.

Two curious consequences follow from the addition of large amounts

of one of the products*, the rate becomes dependent on the concentration

of that product, although it remains independent of the concentration

of the other product, and the reaction orders of the reactants change.

The rate constant also changes but the rate remains proportional to co2.

This has been summarised in Table 1.

It is also interesting to look at the mixture potential. At high

red2 concentration (Case 1), E from eq. (30a) is: m

m - K? + ^ l „ [ ( i / v . m '°x.i' ' ~redi (II-55a)

For Case 2:

E = E2 m (II-55b)

Therefore Em and i appear in a Tafel-like logarithmic relation. Alter-

natively, one could insert the expression of i in eq. (47) into eq. (55a),

and that from eq. (50) into (55b), thus providing the dependence between

39

E and C.. The study of the dependence of E and i on the C. in these m j m m j limiting conditions provides further evidence of the operation of the

electrochemical mechanism.

TABLE II-l. KINETIC PARAMETERS PREDICTED FOR TOTAL MASS TRANSPORT CONTROL.

Reaction orders w. r. t. Condition Reactants Products Rate Constant

ox 2 red x red 2 ox J

No Added Product

Vredi + v J + V , oa ! red 2 o*j red2

0 0 oxx red2

V V ox 2 redi Vred2

k oxx Added red2 V V OX J. ox x V0x i 0 k oxx

Added oxx VOX2

Vredi 0 k , K 1 / V r e d 2 red 2 Added oxx V V red2 red2 Vred2

k , K 1 / V r e d 2 red 2

A minor point should be mentioned here. It is that E is not the m

same as the final potential that would be reached when the reaction

reaches equilibrium in the bulk of the solution too. The reason is that the

surface concentrations are dictated partly by the rate of mass transport.

Thus, for example, if one starts with zero initial concentration of

products, their relative surface concentration at any given time

C° < is not v , h Q X , but [(1 + i /L )/(l + i /Lox ) ]v /vQX . red2 i red2 i m red2 m oxi red2 i

40

Limiting Current Region. 24

This situation has been discussed by Spiro. It arises when the

mixture potential is in the limiting current region of one of the

couples. The rate is then given by the

Levich equation (10). The main features of the catalytic rate are:

(i) linear dependence of u on a)2 ; (ii) first order dependence of Cat

the rate on the concentration of the transport-limited reactant\

(iii) independence on the concentration of the other reactant. Such

behaviour would add value to the hypothesis of an electrochemical mechanism.

The ideal proof would lie in obtaining the full i-E curve of one of the

reactants from i -E data alone, by continuous variation of the concen-m m tration of the other reactant. This curve should coincide with the

electrochemical i-E curve.

e) Suggested Tests for the Electrochemical Mechanism.

Some simple qualitative tests could be performed. Catalysis should

be observed if each couple in turn is replaced by another couple known

to indulge in the electrochemical mechanism with other reaction partners.

The substitute couple should be similar to the one replaced in i and E°

values. The rationale for this test is that the electrochemical mechanism

does not require interactions between the reactants other than the ability

to receive and donate electrons to an electrode.

The electrochemical mechanism can be discarded if polarisation of

the catalyst a few millivolts away from E produces no appreciable m effect on the rate at which product is formed. However, polarisation may

alter the surface activity of electrochemically active participants, even

in the absence of an electrochemical reaction pathway, which would then

produce changes in the rate. For example, many liquid phase catalytic

hydrogenation reactions on platinum involve only chemical interactions

4 1

between the adsorbed organic stuff and H-atoms, the catalyst potential rev

being close to E^ . Anodic polarisation would probably decrease

the H-atom coverage, hence the rate; the effect of cathodic polarisation

would depend on whether the increased coverage actually displaces the

organic adsorbate, or drives 0H to more favourable values.

f) Final Comments.

There are some problems regarding the use of Butler-Volmer equation

in Section II.2.a and b as follows:

Eqs. (15) or (19) describe the initial stages of the reaction, before

the back reaction becomes significant enough due to accumulation of

products. It is assumed that the products do not intervene in the

forward electron rates [eqs. (2) ]. Extrapolation to zero time yields

the product-free initial rate, if no product was deliberately added. rev

But at zero time the E^ values are not defined, according to eq. (1-9).

Therefore, the i0j are also undefined and meaningless. To overcome the

problem one could initially add minute amounts of the products to the

reaction mixture (thus providing a token answer) and in practice such

amounts are likely to be present as impurities; but it would not dispel

doubts about the behaviour of the system as these amounts are reduced

to zero.

An unequivocal definition of i and Em is provided by the Butler-

Volmer equations! ^ W w o x

i = Fki[redi ] r e c U exp[ (l~a1) Zif E ] - F ^ o x ^ 1 exp(-aiZ1f E ) (II-56a)

m a m a m

w 0 x _ W i = Fk2[ox2] 2 exp(-a2Z2f E ) - Fk~2[red2] 2 exp[ (1-a.) Zaf E ] (II-56b) m a m a * * m

42

Eqs. (56) provide a set of two equations with two unknowns (i , and m

E ), which define these quantities in terms of all the other parameters m at any time, i is also contained in the C^ terms if there is partial m 3 control by mass transport. Eqs. (56) can be cast in a useful form.

If reaction (1) is allowed to reach equilibrium (t = : A - A

E = E, and C. = C., i = 0 (H-57) m J 3 m

The cap indicates that equilibrium quantities are being considered. The

equilibrium exchange current densities i 0 j are:

- wred, ^ A wo* ioi = Fk^EredJ exp[ (l-«i) ZifE] = FkxLo^i] 1 exp^a^fE) (II-58a)

W0X ^ ^ W i02 = F k 2 [ 2 ] 2 exp(-a2Z2PE) = Fk2[red2] 2 exp[(l-a2)Z2fE] (II-58b)

Introducing these expressions into eqs. (56):

i = ioxte , exptd-ajJZif AE] - 3ox exp(-a1Z1f AE) ] (II-59a) m red! i

i = ioa[3ox exp(-a2Z2P AE) " 3 , exp[ (l-a2) Z2 F AE] ] (II-59b) m 2 red2

W. AE = E - E ; 3. = (C?/C.) 3 (11-60) m J 3 3

Both couples may be represented in terms of a single " over-potential" , A

AE, and i0-; values which are constant in time, although all of the C. -* 3 vary during the reaction. This should be an advantage for numerical

calculations. Only the 3. and AE (and of course, i ) are time dependent. 3 m

Expressions (59) should also facilitate quantitative consideration

of the latest stages of the reaction, because as AE approaches zero the

exponential terms can be linearised.

4 3

Eqs. (59) are only a different representation of the Butler-Volmer

equation without the ambiguities contained in representations like

eqs. (15) or (19). Identical results should arise from their application

regarding the dependence of i^ and E^ on various experimental parameters.

44

CHAPTER THREE

ELECTROCHEMISTRY ON PLATINUM AND GLASSY CARBON

111.1. Introduction.

Part of this work is concerned with the effect that the nature

of the catalyst and the state of its surface has on the rate of

reaction (1-1). In this chapter the electrochemical properties of

platinum and glassy carbon that are of interest for this work will

be briefly reviewed: the formation and stability of surface films,

and the electrode kinetics of the Fe(CN)! /Fe(CN)e and I /I2 couples.

111.2. Surface Films on Platinum.

The presence of adsorbed oxygen and hydrogen can be revealed by

cyclic voltammetry (see Section IV.2.b). Figure 1 is a typical cyclic

voltammogram of platinum in 0.5 M H2S0A. Its main features have long e.g. 2511?

since been explained. ' ' Starting from ca. zero volts in the

anodic direction, the first threepeaks correspond to the oxidation of

previously adsorbed hydrogen, followed by the so called " double layer

region" in which the low currents are due to double layer charging.

In this potential region the surface is free both from adsorbed hydrogen

and oxygen. At about 0.8 V the current rises again due to the adsorption

of oxygen-containing species from the water to form a layer of so-called

platinum oxides, a process which continues beyond 1.4 V. Oxygen evolution

starts at about 1.5-1.6 V. There is a large degree of hysteresis between

Un

46

oxide formation and reduction. The latter only happens at ^ 0.8 V

after reversal of the sweep into the cathodic direction. The area

under the oxide reduction peak (after correction for double layer

charging current and IR distortions, see Section IV.3.b) is a use-

ful measure of the amount of oxide formed during the anodic sweep.

This peak overlaps with the double layer region, after which there

appear the cathodic peaks corresponding to H-atom deposition from the

solution.

The main point to observe from this is the wealth of different

surface films to be obtained by just holding the potential of the Pt

electrode at varying values in acid solution, and to point out the

need of considering their possible influence on the catalytic properties

of the metal towards redox reactions.

A considerable amount of information now exists regarding the

mechanism of formation of the surface films both in acid and alkaline

solutions. Hydrogen atoms appear to adsorb on the metal with varying

degrees of bond strength, thus giving rise to the appearance of discrete 26 adsorption/desorption peaks in the cyclic voltammogram. About six

26

different forms of adsorbed hydrogen have been observed. They do not

appear to be related to particular crystallographic orientations of the

metal grains, as multiple adsorption/desorption peaks are observed with 27 single crystal faces. It is believed that the Pt-H bond is dipolar,

with the negative end pointing towards the solution. The adsorption of

anions tends to destabilise the H-layer, thus reducing the coverage of 28

H atoms, while cations tend to stabilise it. At high H coverages,

some of the dipoles change their orientation.

47

The oxidation of platinum (and of other platinum metals and gold),

although much studied, has again been recently investigated by 29

Angerstein-Koslowska, et al. These workers propose an oxidation

mechanisms common to all these metals, the differences between them

being due to anion adsorption effects. According to them OH is first

adsorbed at about 0.8 V, forming a monolayer at about 1..05 V. Reversi-

bility of the layer decreases as it grows due to the stabilising effect

of hydrogen bonding. At higher anodic potentials a place exchange

between OH and Pt takes place with simultaneous oxidation to 0 species

and thickening of the oxide film. Anion adsorption acts by displacing

OH from their adsorption sites due to lateral repulsion and occupying

adsorption sites of the OH species, thus causing them to be adsorbed

at higher anodic potentials. This and lateral repulsion increase the

rate of place exchange. The anio n adsorption tends to stabilise the

re-arranged layer, and to change the interfacial electrical field in

a way that facilitates place exchange. 30 More recently, however, Bagotzky and Tarasevich have suggested

a model of oxygen adsorption that appears to differ from that of 29

Angerstein-Koslowski, et al., mainly in that it does not contemplate

place exchange between Pt and 0 or OH species. Hysteresis in the cyclic

voltammograms is due, according to this model, to change in the heat

of adsorption of the adsorbed species, manifested through a change in

the interaction parameter, g, in the adsorption isotherms (see Section

1.3). One might venture to point out that since oxide grows on Pt, not

only as a consequence of increased geometric coverage, but also because

of some form of oxygen penetration into the crystal lattice, allowance

must be made for this in any model. Both groups seem to agree that

48

increased irreversibility (hysteresis) of the oxide reduction peak,

both with time and with an increase in anodic potential, indicates

strengthening of the oxide layer.

In the present work, the platinum electrode was pre-conditioned

in H2SOz» and then transferred to another vessel for further electro-

chemistry or catalytic experiments (see Chapter VI). Therefore, it is

of interest to consider what happens to the surface (whether it has been

covered by an oxide layer, H-layer, or laid bare in the double layer

region), first, upon returning the potential to open circuit; second,

upon exposing the electrode to the air; and third, upon introducing it

into the reaction mixture.

The H-layer may well be destroyed by reaction with adsorbed

atmospheric oxygen to form water. It would then be replaced by a

layer of weakly adsorbed oxygen, just as it would happen if the surface

had been " cleaned" in the double layer region.

The fate of the oxide layer is more problematical. In the apparent

absence of published data regarding the open circuit behaviour, the best

guide would seem the Pourbaix diagram for platinum. However, no definite 31

stoichiometry can be assigned to the surface oxide layer ; besides, the

activity of surface compounds surely differs from that of the bulk

material on which the Pourbaix diagrams are based. The fact that electro-

chemical oxide reduction is very irreversible would suggest that the

oxide, once formed, will remain stable in the acid after the potential

is returned to open circuit (in the absence of strong reducing agents

like hydrogen gas). The same is even more true when the electrode is

exposed to air or to the nearly neutral reaction mixtures. The point

will be examined again in Chapter VII.

49

III.3. Electrochemistry of Fe(CN)| /Fe(CN)e arid of I /I2(I3) on Platinum.

a) The Fe(CN)e /Fe(CN)e couple has been investigated by a 32

number of authors. Jahn and Vielstich obtained values for the

standard rate constant and transfer coefficient of 0.05 cm s and

0.61, respectively in 1 M KCtf at 25°C, using the RDE. Daum and Enke33

have carried out a careful study using the current impulse technique,

in 1 M KC€. The cathodic reaction is first order in ferricyanide and

the anodic one also first order in ferrocyanide, in a concentration

range of over 100-fold. On a reduced electrode (i.e., oxide-free) the - 1 - 1 standard rate constant is 0.24 em s , and 0.028 cm s on an oxidised

one. The transfer coefficient is close to 0.5. The activation energy

of the exchange current density was 3 A 9 Kcal mol \ irrespective of the

state of the surface. Daum and Enke have pointed out that their results

indicate nothing other than a simple electron transfer step. In a later 34

study Blaedel and Schieffer using turbulent tubular electrodes have

confirmed these results. Measurements of the reversible potential of

this couple in solutions of varying concentration of potassium salts 35 have led Hanania, et al., to conclude that there is a significant

amount of ion pair formation between the cations in the solution and

the ferr(i/o)cyanide species. This raises the question of identifying

the species involved in charge transfer in the electrode kinetics, and in general in any reaction in which these species participate. Peter,

36

et al., found that the cations influence the rate in the order

L^ < Na+ < K+, Cs+ . The activation energy of the electrochemical rate

constants is independent of the concentration of the supporting electrolyte,

50

but the pre-exponential term in the Arrhenius equation varies linearly.

They have, therefore, proposed that the activated complex is formed

after one cation collides with an already cation-associated ferr(i/o)-

cyanide molecule. These results were obtained on gold electrodes, but

they are of obvious relevance to any electrode material at which this

couple is studied. A complementary study on the effect of the anions

of the supporting electrolyte has been done by Kulesza, Jedral and 37

Galus on platinum. At constant sodium salt concentration, the

rate is increased in the order F~ < CNS~ < SO* < CH3C00~ < C^oZ <

POA < N03 < C-6 < Br , but the increases are small and seem to be

related to the increase in the formal potential of the couple and to

the change in the potential of zero charge of the electrode. Thus,

the anion effects do not appear to be specific to this couple.

It is convenient to point out that the standard rate constant

for this couple is relatively large which makes it highly reversible.

The study of its electrode kinetics is almost certainly bound to be

complicated by mass transport if steady-state current voltage curves

are used as a means of study.

Association with the cation may affect the limiting current density

of ferr(i/o)cyanide due to an increase in the size of the electroactive

species, which tends to reduce its diffusion coefficient according to

the Stokes-Einstein equation: D = kT/67rnr (III-l)

where ri is the viscosity of the solution and r is the radius of the

38 hydrated ion pair. Muller and Sohr obtained a straight line for plots

Ccv-l|0* C0r>C £v\4 l-*.4f'on.

51

+ + + of D vs. 1/r for the chloride salts of Li , Na and K . The diffusion

coefficients were obtained from the limiting current densities at a

platinum RDE. b) The kinetics of the I /I3 couple in H2S0*, at platinum have

39

been studied by Vetter by the faradaic impedance method. By obtaining

the concentration dependence of the anodic and cathodic current densities

the following mechanism was proposed!

I~ a*. I + e~ (r.d.s.) (III-2a)

21 ^ I2 (III-2b)

I2 + I~ ^ 1 3 (III-2c)

where step (III-2a) is rate determining. This mechanism gives rise to

the observed concentration dependence of the current: _

i = Fkbrds(K1K2)5[i;]T[l"]iexp(-afE) - Fk^tl"] exp[(l-a)fE] (IH-3)

where Ki is the equlibrium constant of step (2j>) and K2 that of step (2c) .

This mechanism was confirmed by Newson and Riddiford by the RDE technique, 40 who have also concluded that coverage by iodine atoms is insignificant.

Using the impedance method to determine the concentration dependence of 41

the exchange current density, Dane, Janssen and Hoogland have considered

the sequence! I~ » I , + e~ (III-4a) ads

I , + I~ > I 2 + e~ (r.d.s.) (III-4b) ads I2 + I~ » la (III-4c)

They concluded that (4b) is the r.d.s., and that the coverage by iodine

is significant. The resulting rate law is given by:

52

i = FMl 3j[l J 1 exp(-afE) / [ 1 + K ^ L l ] exp(fE) ]K-

-Fklrj exp[(l-a)fE]/[l + K^tl"]"1 exp(-fE)] (III-5)

where K , is the ratio of the foward and backward rate constants of ads step (4a), and K is the equilibrium constant of (4c).

The electrodes were not prepared in the same way by all the authors.

Vetter does not seem to have applied any particular pretreatment; Newson

and Riddiford polished their RDE with Cr203 prior to each run without

subsequent conditioning, which rendered the surface probably oxide-free.

Dane et al. state ambiguously that their electrode was subjected to

alternate cathodic and anodic polarisation (and stored for two hours in 42 43 solution of iodide and iodine). Barbasheva, et al. and Povarov, et al.

who worked with an oxidised RDE obtained rate laws consistent with the ^ 41

mechanism of Dane et al. They also agree on the presence of significant

coverage by electrochemically active iodine. However, it is still

necessary to reconcile these opinions on iodine coverage On oxidised 44 platinum with the findings of Schwabe and Schwenke, and of Hubbard, 45 Osteryoung and Anson that iodine and iodide do not seem to adsorb in

significant amounts on oxidised platinum although they do so quite strongly

on reduced platinum. Results on the isotopic exchange of iodide and 46 iodine point to the same conclusions.

47 Bejerano and Gileadi have studied the formation of thick layers

of iodine during the anodic oxidation of iodide. If the bulk concentration -3

of iodide exceeds ca. 5 x 10 M, the iodine produced in the limiting

current density region precipitates at the electrode surface because its

concentration exceeds its solubility in the solution. The iodine film

53

hinders the transport of iodide and the limiting current falls to a

lower, steady state value governed by the rate of dissolution of I2,

the transport of I3 and the transport of I across the film. The

current is still proportional to OJ2 because the transport of iodide

from the solution to the film is still controlled by mass transport.

III.4. Surface Films on Glassy Carbon.

Glassy carbon is an amorphous material obtained by calcination

of organic material, mainly cellulose, which does not pass through a

liquid or semi-liquid s t a t e . T h e r e are short range ordered regions

of ribbon-like shapes with the graphite structure. These ribbons

are randomly oriented and poorly stacked which leaves empty regions or

pores, forming about 30% of the volume of glassy carbon. As a consequence

its density is only about 1.5 g cm 3 compared with 2.2 g cm 3 for 49

graphite. Glassy carbon is an isotropic material with respect to

several physical properties, in particular towards electrical conductivity,

which is an advantage over graphite for electrochemical work. Its — —3 resistivity is about 6 x 10 3 0 cm, higher than graphite 10 Q cm),

—6 —5

and certainly much higher than that for metals (10 - 10 ft cm), which

makes glassy carbon (and graphites in general) slightly semi-conducting.

Indeed, the overlap between the conduction and valence bands in graphites 48b is only about 0.6 eV. Therefore, one would expect smaller electro-48b chemical rate constants on carbonaceous electrodes than on metals.

Hydrogen evolution is irreversible on glassy carbon, as on all -7 -2 49 carbonaceous materials, with 6.8 x 10 A cm exchange current density

-3 50 (cf. ca. 10 A cm-2 on platinum ). Scarcity of adsorption sites from

hydrogen atoms has been proposed to explain this."^ On the anodic side,

54

oxygen evolution proceeds above the oxygen equilibrium potential with 48c

evolution of C02. Thus, glassy carbon does not become covered by

oxide films in the anodic region. However, there is the possibility of

creating chemical groups on the surface either by electrochemical or 52 chemical treatment of the electrode. For example, Mamantov, et al.

report the existence of a reduction peak at ^ 0.35 V (vs. SCE) in H2SCU

on pyrolytic graphite upon application of a potential sweep. The peak

height increases with an increase in the value of the potential at which

the electrode is pre-anodised. Also, the cyclic voltammograms of , v 53 graphite obtained by Majer, Vesely and Stulik reveal an anodic wave 54

with Ep^ % 0.9 V (SCE), at pH 7.59. Taylor and Humffray found that

oxidising pre-treatment of their glassy carbon electrodes either with

concentrated H2S0* or with chromic acid led to increased rate constants

for the Fe(II)/Fe(III) and for the Ce(III)/Ce(IV) systems. The

capacitance also rose from 25 yF cm 2 for untreated electrodes to

250 yF cm 2 for chromic acid-treated ones which pointed to an increase

in the adsorbed charge or of charged groups at the surface. It seems

that the presence of chemically active surface groups on carbonaceous

materials is generally accepted^** although there is disagreement

concerning their nature. Electrochemically, these groups are undoubtedly

important. In molten salts they seem to be partly responsible for the

currentless deposition of precious metals in solution in the melt"*"*

(a process which is probably under mixed potential control).

III.5. Electrochemistry of Fe(CN)g /Fe(CN)s" and I~fll on Glassy Carbon.

As with the previous section, evidence obtained on other carbon-

aceous materials will be considered too.

55

5 A 34 a) Taylor and Humffray and Blaedel and Schieffer have reported

that the rate constant for the ferr(i/o)cyanide system is about 10

times lower on glassy carbon than on platinum. The former authors report

cathodic and anodic transfer coefficients close to 0.5, while the

latter often found a = 0.8 and a = 0.22. Blaedel and Schieff er cath an

attribute their results partly to adsorption of the electrodctive species

on their glassy carbon electrodes in accordance with the findings of 56

other authors. It should be pointed out, however, that in the analysis

used Blaedel and Schieffer assume a first order dependence in the

concentration of the electroactive species which was not found to be 56 true on a graphite electrode by Sohr, Muller and Landsberg. These

authors reported that the order in ferricyanide for the reduction and

in ferrocyanide for the oxidation was approximately 0.7. The anodic

and cathodic transfer coefficient are both approximately equal to 0.2.

The oxidation current of ferrocyanide also depends on the concentration

of ferricyanide, which is the electrochemically inactive species. They

have interpreted their results in terms of the formation of a complex

between the oxidised and the reduced species, linked by a cation from

the supporting electrolyte, which adsorbs on the electrode. The complex

undergoes electron transfer more easily than either of the monomers.

On graphite RDE (and also on the perovskite mixed oxide La0 .8Sr0•2C0O3) 57 Beley, Brenet and Chartier found that preceding the charge transfer

step there must be ion pair formation between a cation from the

supporting electrolyte and a molecule either of ferro or ferricyanide,

which subsequently adsorb on the electrode. Their conductimetric results

also indicate that ferrocyanide forms ion pairs more easily, without

56

water molecules interposed between the partnersI in the case of ferri-

cyanide one water molecule separates them. However, they did not 58 explore the possibility of complex formation. More recently, Muller

59

and Muller and Dietzsch have re-interpreted their results by

proposing that the one electron transfer occurs by two successive

partial charge transfer steps, a mechanism that would be made possible

by adsorption of the electroactive species. They have substantiated 59 their claim experimentally by showing that the exchange current

density calculated from their mechanism agrees with the measured one on

pyrolitic graphite over a 10^-fold range of the ratio [Ox]/[Red].

However, one would like to know whether this proposed mechanism is in

agreement with the quantum properties of the electron or if it is

consistent with transfer to an adsorbed complex.

b) Relatively little work has been carried out on the kinetics

of the I /I3 couple on glassy carbon. There is some work on the over-6 0 all electrode reaction in conditions of total mass transport control. 61 On flow-through graphite electrodes Wroblowa and Saunders concluded

4kc 49 thatlmechanism proposed by Vetter on platinum is also operative here

(eqs. 2a-c), with low coverages by atomic iodine and transfer coefficients

close to 0.5.

57

CHAPTER FOUR

TECHNIQUES AND INSTRUMENTATION

IV.1. The Rotating Disk Electrode (RDE).

a) The Ideal RDE.

In the present work the platinum and glassy carbon catalysts

(used as electrodes too) have been fashioned as rotating disks, following

the common practice in electrochemistry when mass transport limitations

are present. 62

The theory of the RDE has been rigorously worked out by Levich

for a smooth disk of infinite radius rotating in an infinite volume of

incompressi ble fluid, the disk arranged so that gravity acts perpendicularly

to the disk, in steady state laminar flow. Figure 1 is a diagram of

the ideal RDE, showing the velocity components Vy, V , and V^ (perpen-

dicular to the disk, in the direction of the disk radius, and perpen-

dicular to the disk radius, respectively). Rotation causes the layers

of fluid next to the disk to be dragged along and swept away along the

radius. Since the fluid is incompressible (that is, unstretchable) mass

moves in from the bulk towards the disk to replace what was swept away.

The net effect of rotation is the sucking of fluid towards the disk and

its throwing away along the radial coordinate in a swirling motion.

Figure 2 shows the dimensionless velocity components as a function of

the dimensionless distance from the disk surface,y = (co/v) 2y. At y = 3.6

the y component reaches about 0.8 of its bulk value while the other two

are nearly zero. Therefore, the distance 6 = 3.6(v/u))2 is defined

Figure IV-1

Figure IV-2

59

as the layer of liquid dragged by the disk, the Prandtl or momentum 23

boundary layer. If some of the material is consumed at the surface

there will be a concentration difference between the bulk of the

solution and the disk surface. However, Figure 2 suggests that a

concentration gradient will only extend a short distance from the

surface, inside 6p, due to mixing produced by considerable mass

movements. Figure 3 shows the form of this gradient as a dotted

line, and the equivalent Nernst diffusion layer of thickness <5„ = N JL i _ JL

1.61B| v^ 03 2, through which the consumable species, j, may be considered

to cross by diffusion alone. From this result the Levich equation

(11-10) may be derived. _ JL The ratio 6„/S =0.42 D! V 3 is independent of u>. Its value is N P j -5 2 -1 -2 2 -1 ^ 0.05 if D_. 10 cm s , and v ^ 10 cm s , which are typical

values for aqueous solutions. This confirms that the Nernst diffusion

layer is deep inside the momentum boundary layer.

Two points are worth noting. First, both and are independent

of the radial distance (this is because V^ is also independent of it).

Thus, all of the disk surface is uniformly accessible to the reactants

in the fluid, and the current density is uniform all over the disk.

Secondly, the thickness of the diffusion layer, can be precisely

and reproducibly controlled by the rotation speed of the disk. Also,

once a steady state is established (which only takes less than a few

seconds), remains invariable with time. Abundant confirmation of 63 Levich's theory exists in the literature.

60

1/3 1/2 y/[(D./v)(v/OJ)]

Figure IV-3

Figure IV-4

6 1

b) The Practical Rotating Disk Electrode.

In practice the RDE consists of polished disk of material embedded

in an insulating mantle, as shown in Figure 4a and 4b. It is important

to know how to design a RDE so that its behaviour is close to the

Levich one.

One of the features of the Levich electrode is that mixing of the

fluid on both sides of the disk is avoided by its being of infinite 23

radius. This condition is best met by mantle shapes as in Figure 4b,

because mixing tends to occur in a horizontal plane away from the

electroactive disk (cf. lines of flux in Figured). For this very reason

the radius of the mantle should be large compared to the radius of the

disk to allow the mantle to act as a " hydrodynamic insulator" . There-

fore, the " trumpet-shaped" form in Figure 4b was adopted in the present

work.

Uniform accessibility of the surface is true only in an approximate

sense. For a disk of finite radius, diffusion at the edge takes place

not only from a distance perpendicular to the surface, but from the

sides too. Therefore, the current density tends to be larger at the

edge. The effect is minimised if is much smaller than the radius

of the disk, i.e.,

Another effect is connected with the solution having a finite

resistance R^. There will be a potential drop between the RDE and the

counter electrode, the equi-potential lines not being parallel to the

surface (see Figure 5). In this situation the current distribution on 64 the surface of the electroactive disk is

6 /R £ 0 N

(IV-1)

I i = 2vk/iT(R2-r2) 2 (IV-2)

62

Primary Current Di stribution

Figure IV-5

X3 O

Figure IV-6

63

where v is the voltage difference between the RDE and the counter

electrode, k is the conductivity of the solution, and r is the radial

distance measured from the centre of the electrode. However, consid-

eration of electrode kinetics produces a more uniform current distri-

bution if:

di/dE < 0.36 r k (IV-3)

where di/dE is the slope of the i-E curve. There is always uniform

distribution at the limiting current since here di/dE =0. In solutions

of low conductivi ty or with small electrodes, oneshould avoid working

near the half wave potential (Ej ) where di/dE is at its highest value. 2

It has been found that the flow changes from laminar to turbulent

when the Reynolds number, defined for a rotating disk as Re = o>R2/v 5 63

reaches the value ^ 2 x 10 . This sets an upper limit to the

rotation speed o>: •J O _ 1

03 < vRe crit./r2 ^ 2 x 10 cm s /R2 (IV-4) max

-2 2 -1 taking v as 10 cm s for aqueous solutions. However, turbulence

may start at values much lower than o) if the disk vibrates axially max y

or laterally.

The lower rotation limit is dictated by the need to ensure that a

natural convection does not become significant compared with forced a ^ 21,61 - # . convection. Authors, use to express this condition as:

Sp/R 0 (IV-5)

It is not clear why this should be so. Indeed, for a Levich disk eq. (5)

is true at all speeds, yet at low 03 values one would expect that convection

64

would affect the flow. Certainly, one must recognise the need to have

a small Sp or i.e., more or less large u) values, so that forced

convection overshadows natural convection; but one would expect the

corresponding condition to contain parameters characteristic of both

transport processes.

The problem of mass transfer to an excentric disk electrode has 66

been considered by Mohr and Newman. It appears that excentricity

is not important if the centre of the disk is off the centre of rotation

by less than 64% of the radius length, which is a condition easily met

by large electrodes. Smaller disks, say less than 1 mm in radius, are

more prone to this abnormality since small absolute excentricities are

easily of the same order of magnitude as the radius. It is certainly

of no consequence for our large electrodes (> 2 cm radius).

c) Uses of the RDE.

The reasons why one would wish to use a RDE for electrochemical

systems involving partial mass transport control are ! (i) mass transport

is rigorously described by the Levich theory; corrections due to non-

ideality of practical disks can be worked out by more refined numerical

calculations of the theory itself; (ii) introduction of mass transport

into electrochemical equations is easy, and allows measurement of fast

electrode processesprovided that the heterogeneous rate constant, k, is 67a no larger than 0.1D./6 . (iii) The fact that the RDE is a flat disk J N

embedded in a flat mantle allows it to be cleaned by polishing without

changing the electrode geometry.

65

IV.2. Current-Voltage Curves.

The purpose of the recording of steady state i-E curves in this

work has been two-fold: to obtain the values of mixture current and

potential in order to compare them with the corresponding catalytic

values, and to try to obtain kinetic parameters of the couples to

introduce into the corresponding theoretical rate expressions. Some

cyclic voltammetry experiments have also been carried out to investigate

(mainly qualitatively) the adsorption of reactants on the electrode. The

basis of these techniques are explained here.

a) Steady State Recording.

This method simply consists of setting the potential of the electrode

under study (working electrode, WE) at a fixed value against a reference

electrode and noting the current when it has reached a constant steady

state value. The entire i-E curve is thus obtained point by point. If

the electrode process is very reversible, and if a RDE is used, the steady

state can be attained in a matter of seconds.

b) Potential Sweep Methods.

This technique exploits the time lag needed for the steady state

to be reached by diffusion processes. When the potential of the electrode 6 7b

is scanned continuously the surface concentrations of the electroactive

material adjust to a value dictated by the electrode kinetics. If the scan

rate is fast enough the diffusion layer will not have time to adjust to

its steady state value so that the rate of diffusion is larger than in the

steady state. The current line in Figure 6 will be closer to the Butler-

Volmer line, until it eventually overshoots the steady state limiting current.

66

However, as the scan progresses diffusion also progresses towards a

steady state value, thus bringing down the current to its limiting value.

If the scan is reversed at this point, the product (which is now present

in large amounts at the surface) will begin to undergo the back reaction,

bringing the current down until another peak is produced and the current

finally takes the same value as at the beginning of the scan.

The technique is particularly useful for detecting reaction inter-

mediates as they produce additional peaks in the voltammograms. Adsorptions

and desorption peaks of electroactive, species can be detected too. The 67c

main difference between them is that for reactions not involving

adsorption, JL_

i a v2 (IV-6) P and i a v (IV-7) P

for adsorbed reactantswhere i is the peak current and v is the scan P rate of the potential. For reversible, Nernstian, adsorptions it is

also true that, at 25°C:

E - E , = 90.6 mV/n (IV-8) P P/2

where E^ is the peak potential and E ^ the potential for which i = ip/2.

The anodic and cathodic peaks should occur at the same values. For non-

Nernstian reactions, the positions of the peaks become dependent on In v.

IV.3. Electrochemical Instrumentation.

The basic modes of operation and desirable caracteristics of the

electrochemical equipment, including the electrochemical cell, are described

in this section.

67

a) Potentiostat.

The potentiostat allows the potential of the WE to be kept constant

against a reference electrode (RE) The current necessary to achieve

this is passed between the WE and another auxiliary or counter electrode,

(CE). The basic circuit of a potentiostat is shown in Figure 7a. Its

basic element is the operational amplifier (labelled OP-AMP). It works

by keeping the two inputs (labelled + and -) at the same potential. If

they differ by an amount AV, current flows from the output (apex opposite

to input side) to restore AV to zero. The input impedance is very

large (infinite, for an ideal OP-AMP) so that all of the current flows

between the output (CE) and earthed WE. The potential V(n fed to the

+ input is reproduced at the other input to which the RE is connected.

From the connections it follows that the difference in potential between

the WE and the RE is kept constant. The resistance R connected at the

output allows measurement of the current through the voltage drop

across it. The size of R has no influence upon the current because it

depends only on the potential difference between the inputs. The high

input resistance of the amplifier means that it draws negligible current

(i.e., input bias current) from the cell both during operation and in

standby.

For steady state work it is important that the input bias current —8

(IBC) be of the order 10 A or less, otherwise the WE and RE potential

will be altered due to their intrinsic faradaic resistance. For the same

reason any other measuring device like digital voltmeters (DVM) should

have a very high input impedance. The maximum output voltage between WE

and RE should be as high as possible, and so should the maximum output

R=counting resistor

Figure IV-7

RE

'in ^solufion

A / W V V W V A A A A / V W V

W E CE

Figure IV- 8

69

current. For non-steady-state work (in which V ^ is replaced by ,

or fitted with, a time-varying source like a ramp generator for cyclic

voltammetry, or a square-wave generator for pulse experiments), the

potentiostat must be able to assume the programmed potential values

at a rate at least as fast as the changes in the source output. This

is measured by the rise time of the instrument.

Connection of low impedance recording devices to the inputs of the

potentiostat should be made via a voltage follower (basic circuit in

Figure 7b) which senses the measured voltage while at the same time it

supplies the recorder with the input current it needs without altering

the cell voltage.

b) The Uncompensated Solution Resistance.

Ideally, the reference electrode should be just outside the double

layer of the WE. In practice the RE (or the tip of its Luggin capillary) 17e

has to be placed tenths of millimeters away. Figure 8 illustrates

how the voltage difference controlled by the potentiostat includes a

part due to the effective ohmic resistance R of the solution between

the WE and the tip of the RE. Therefore! Vin = E W E " E R E + I R (IV"9)

where I is the net current. Or, in the more familiar overpotential

notations:

T1 = T1 + IR (IV-10) app

Only a part n of the applied overvoltage is kinetically useful. The

ohmic drop always causes R) to be smaller than TI , and the effect app'

70

is larger the larger the magnitude of I. The effects of the IR drop

can be minimised by: (i) making the supporting electrolyte as

concentrated as possible; (ii) placing the tip of the Luggin capillary

as close as possible to the WE surface (but see next section); (iii)

using low area electrodes, as this reduces the net current at a given

overpotential. The effect on the steady state current-voltage curve

of an irreversible couple is shown in Figure 9a for different values

of R. A similar distortion pattern is found in cyclic voltammograms.

When a sudden voltage step is applied to the WE, the effect of the

ohmic drop is to cause a delay in the attainment of the new potential

by the WE. This is illustrated in Figure 9b.^^ In the absence of

faradaic processes, the WE double layer can be regarded as a capacitor

of fixed capacitance C in series with the solution resistance, R.

Applying ' Ki'rchhof f! s laws to the corresponding circuit (Figure 10),

we have I

where V is the applied potential and q is the WE charge. This is

a simple first order, constant coefficient, non-homogeneous differential

equation. Its solution is,

RC is the time constant of the circuit and allows quantitative assessment

of the severity of the IR delay, if R and C are known or can be estimated.

If the rate constant, k, of the electrode process studied can be estimated,

then the condition

-V = IR + E ^ = Rdq/dt + q/C (IV-10)

(IV-11)

x « RC « 0.69/k (IV-12)

E

Figure IV-9

RC

applied E

electrode response

time

— V M A M / —

Figure IV-10 R c

72

must be fulfilled (if k is a first order rate constant), where T is

the rise time of the potentiostat, or the slewing rate multiplied by

the total applied potential.

c) Cell Design.

Some general design factors common to all electrochemical cells

are:

1) The reference electrode compartment must be fitted with a Luggin

capillary whose tip should be positioned close to the WE surface. The

distance from the WE should not be less than 2 ( ( f ) = outer diameter

of capillary tip) as a screening effect of the electrode potential would

be effected; larger distances produce larger IR drops, so this is an

s optimum distance. If the WE is a RDE the capillary must be placed

vertically beneath the disk, pointing to the centre as this arrangement 23

produces the least disturbance of the flow pattern.

2) It is desirable in principle to have the three electrodes in separate

compartments to avoid contamination of the WE with the reaction products

of the VCE and with the material of the RE. The inter-compartmental

connections should be of low resistance so that the maximum output

voltage of the potentiostat is not reached too soon. This is particularly

important in experiments involving transients.

3) The CE should be positioned with respect to the WE so as to produce

as uniform an electric field as possible. If this is not so, the current

density will not be uniform, nor will the effective solution resistance.

The CE should possess a large surface area compared with the WE.

4) In order to minimise the IR drop and the time constant of the cell,

the actual surface area of the WE should be kept to a minimum in order

to reduce the net current available and the overall capacitance of the > electrode.

73

CHAPTFR FIVE

THE REACTION BETWEEN FERRICYANIDE AND IODIDE IN SOLUTION.

V.1. Introduction.

The reaction between ferricyanide and iodide appears to have been 68

first studied by Donnan and Le Rossignol who found the reaction to be

of second order in ferricyanide and of third order in iodide, at room

temperature. Further research by Just^ and by Wagner^ has shown the

initial rate to be rather of the form:

v, = k[Feic][l"]2 (V-l) hom

This was confirmed by Beckman and Sandved^ who followed the reaction

colorimetrically at 350 nm (where I3 absorbs strongly) instead of

titrating the iodine produced with thiosulphate in the presence of

starch as had been done by previous authors (the so-called Harcourt-

Esson technique). It should be pointed out that the reaction between 72

the iodine produced and iodide ions in solution is extremely fast - k f ^ -

la + I Is , K = k f / k b (v-2) b

with kr = (6.2+0.8) x 109 M_1 s"1 and k = (8.5 + 1.0) x 106 s"1 at r — b — 25°c; therefore, the above techniques at least are not rate-limiting.

The reaction was found to be inhibited by ferrocyanide, and to explain

this Just proposed the mechanism:

Fe(CN) + 2I~ Fe(CN) + I~2 (V-3a)

I~2 + Fe(CN) 6~ la + Fe(CN) (V-3b)

I2 + Fe(CN) 6~ ^ ^ 2l" + Fe(CN) (V-3c)

By assuming that all the forward steps occur at the same rate v^om»

74

v, = ki[Feic][l ]2/(l + k3[Feoc]/k2[Feic]) (V-4) hom

which explains his results. This mechanism was criticised by Indelli 73

and Guaraldi because there was no evidence of the existence of the

I2 ion. They proposed instead the formation of the eight ligand

activated complex, I2Fe(CN)| , with release of an iodine atom and an

iodine ion. In this case one should seek evidence for the existence

of I atoms in solution. 74 Friedman and Anderson seem to have been the first to study the

effect of the concentration and nature of the supporting electrolyte.

They found that K+ ion has a bigger effect on the rate than Na+ ion,

chloride salts being more effective than nitrate ones. A systematic

study has been carried out by Majid and Howlett.^ Their main finding

was that the initial rate can be expressed by: Vhom = kIV[K+][Feic][r]2 (V-5)

IV k appeared independent of ionic strength for variations in the supporting

electrolyte (KN03) between 0.193 and 0.372 M. They proposed the following

mechanism:

K+ + Fe(CN) —^ KFe(CN)2~ (V-6a)

i" + KFe(CN) 2~— — ^ IKFe(CN) (V-6b)

i" + IKFe(CN) >Ia + KFe (CN) 6~ (V-6c)

U + Fe(CN)6~ —>I 2 + Fe(CN) 6~ (V-6d)

with (6c) as the r.d.s., which gives rise to eq. (5). Notice that eq.

(4) can be more conveniently expressed as!

v0/v = 1 + k'[Feoc]/[Feic] (V-7)

where v0 is the rate in the absence of ferrocyanide, v is given by the

full eq. (4), and k' is the combination of the various constants

accompanying the ratio [Feoc ]/[Feic].

75

V.2. Experimental,

a) Apparatus.

The basic experimental arrangement for the homogeneous runs is

shown in Figure 1. The thermostat bath (38 cm depth x 50 cm x 38 cm)

was fitted with side glass windows and lined inside with enamel-painted

copper plates. The outer casing, of cemented asbestos sheet (Sindanyo),

was hollow and filled with Vermiculite as insulation. The bath was

provided with a motor and paddle stirrer, and filled with distilled water.

Since most of the work had to be carried out well below room temperature,

to reduce the contribution of the homogeneous rate, the thermostat was

provided with a refrigerating unit (Townson and Mercer, Ltd., Croydon).

Temperature control was achieved with an Ether control relay, type no.

213 B, fitted with a red rod heater (Electrothermal, 400 Wails) and

connected to a contact thermometer (Jumo, D.B.P., Germany). The

temperature of the bath, measured with a mercury thermometer graduated

in 0.01°C divisions, could be controlled within + 0.02°C of the intended

value.

The reaction vessel was a straight walled 500 ml Quickfit glass

vessel (FV500) , with a flat lip around the upper edge which allowed it

to be placed inside the bath supported by an iron ring fastened to a

bar at the edge of the thermostat. The reaction mixture was stirred by

a Teflon-covered magnetic bar driven by a submersible magnetic stirrer

(Rank Brothers, Bdttisham). Absorbances were measured with a Unicam

SP 1800 ultraviolet Spectrophotometer. Readings in the range of 0.001

to 2.00 could be made with accuracy ranging from 0.001 to 0.01, depending

on the particular scale used. Quartz cells of 4 cm optical path length

were used.

CC: cooling coil CU: cooling unit H : heater M : motor MS: magnetic stirrer RB: relay box RV: reaction vessel T : thermoregulator

Figure V-1

77

b) Chemicals.

The chemicals were all of Analak grade and were used without further

purification: K3Fe(CN)6, KN03, KC/, H2SO*, NaOH, and iodine (resublimed)

from BDH; K^Fe(CN)6.3H20, soluble starch and As203 from Hopkin and

Williams Ltd.; KI from May and Baker. Solutions were prepared in

distilled water; those to be used for kinetic runs contained already

the supporting electrolyte (i.e., KN03, or KCO, and were equilibrated

inside the thermostat before filling the graduated flasks up to the mark.

The solution with the greatest volume, usually that of KI, was then

passed through a Quickfit SF3A33 sintered glass filter to remove

suspended solids, and stored in a clean stoppered Pyrex glass bottle.

c) Measurement of Extinction Coefficients.

The extinction coefficient of I3, either in 1 M KN03 or in 1 M KC^,

was obtained from the slope of the plot of the absorbance vs. the

concentration of diluted samples of a standardised iodine solution.

The standardisation of the stock iodine solution was carried out with

slightly basic As203 solution according to the procedure cited in the

literature,^ the concentrations of I2 and As203 being ^ 0.1 M. The

reaction is:

H2As03 + I2 + 2HC03 ^H2ASO^ + 2I~ + H20 + 2C02 (V-8)

Aliquots of 20 ml of the As203 were titrated with the iodine solution

in a 25 ml burette (grade B) with an accuracy of 0.05 ml, but the actual

volumes could be estimated to within 0.025 ml by eye. The titrations

themselves were in the absence of KN03 or of KC^. The stock solution KNO was diluted 20-fold for eT- 3 or 200 fold for zZ- with 0.241 M KI. 13 i 3

Samples were taken from this solution to prepare a series of dilutions —6 —6 whose [l2] ranged from ^ 1 x 10 to ^ 15 x 10 M. These solutions

78

contained either 0.241 M KI, plus enough solid salt to give 1 M KN03,

or 0.0167 M KI plus enought solid salt to reach 1 M KC/. The absorbances

were obtained in 4 cm cells against a blank containing the background

solution.

To measure the extinction coefficient of molecular iodine, about

50 ml of 1 M KN03 were stirred overnight at room temperature with some

crystals of iodine, and its absorbance read against 1 M KN03. The

iodine concentration was obtained from the absorbance of a 1:21 dilution

with 0.241 M KI in 1 M KN03 and the previously determined . I3

The extinction coefficient of ferricyanide was obtained from the - 3

absorbance of a 2 x 10 M solution in 1 M KN03, read vs. 1 M KN03.

d) Typical Homogeneous Run.

A typical homogeneous run is one started in the absence of added

products, at (say) 5°C. First, 200 ml of the stock KI solution measured

with a 100 ml volumetric pipette were placed in the reaction vessel, and

stirring started. The reaction was initiated by adding 10 ml of K3Fe(CN)6.

Samples of 5 ml were taken at 10 minute intervals with pre-cooled

volumetric pipettes (grade B) which had been kept inside a 250 ml cylinder

almost completely submerged inside the thermostat bath. The samples

were diluted with 10 ml of pre-cooled supporting electrolyte solution in

order to quench the rate [according to eq. (1), a 3-fold dilution should

produce a 27-fold decrease in the rate]. However, if the reaction was

to be carried out close to or above room temperature, neither pipettes

nor diluent were warmed. The spectrophotometer cell was rinsed with the

diluted sample before filling it completely, and the absorbance read

against a reference cell filled with a ferricyanide solution diluted so

as to compensated roughly the background absorbance of the diluted

sample at 350 nm.

79

If added iodine or ferrocyanide were to be present from the start,

200 ml of stock KI or ferricyanide solution respectively were first

placed in the reaction vessel. A 4 cm2 platinum electrode was immersed

in the solution, which was connected by an agar bridge (0.6 g Agar in

20 ml supporting electrolyte) to a beaker containing supporting electro-

lyte solution and a 55 cm2 platinum counter electrode. The electrodes

were connected to the potentiostat (the latter arranged for galvano-

static operation), and a constant current passed for a fixed period of

time, monitored by the voltage drop it produced across a decade

resistance box (Croydon Instruments Ltd., 0.1%) connected to the potentio-

stat (Figure IV-7a). For example, if 1.2 x 10 M iodine had to be

present in the final 210 ml of reaction mixture, 1.013 mA of current

were passed for 8 minutes through the initial 200 ml of KI solution,

under constant stirring; for this purpose the potentiostat had been set

to give a drop of 405.3 mV across 400 ft (+ 0.1%), on the resistance box.

V.3. Treatment of Kinetic Data.

Since the reaction was followed by the appearance of I3, allowance

must be made for its dissociation into I2 and I , for the change in the

absorbance due to the appearance of Fe(CN)s and free I2, and for the

disappearance of Fe(CN)e and of I . With reference to Table 3, the

total absorbance A of the diluted sample is given by Beer's law as:

A = Aei;[i;] + e [Ia] + eFeoctFeoc] + eFeic A[Feic]) (V-9)

where -6 = optical path length, and A[Feic] is the change in [Feic]. From

the stoichiometry of the reaction and the expression for the equilibrium

constant of reaction (2)I

80

A = + e I , / K [ n + 2(eFeoc " £Feic)][i;] (V"10)

77 Values of K were obtained from the work of Katzin and Gebert in

1 M HC Oz, and are given in the following table:

TABLE V-l.

T/(°C) 20 25 30

K/(mol 877.2 7kQ-7 699.3

The data are well represented by the equation (fitted by least squares)

K = 0.8763 exp(2020.2/T) (V-ll)

with a correlation coefficient of 0.96 (T is the absolute temperature

in °K). From eq. (11) the values of K at other temperatures were found

to be:

TABLE V-2

T/(°c) : 5 10 15

K/(mol 1250 1100 972

[I J varies between 0.01 and 0.1 M in the diluted sampleJ this and the

values of the extinction coefficients in Table 3. cause e - to be the J-3

only important contributor to the total absorbance.

The total iodine in the dilution is: total

[ l z 3toLl = [ l 2 ] + [ I® ] = (1 + = (V~12) where

f = 1 + 1/K[I~] (V-13)

81

Introducing eq. (12) into eq. (10), and neglecting the (e„ -e_ . ) reoc reic term (see the next section)I

,dil total' e*PP = eT-/f 1 2 J-3

(V-14)

RM

where [ 12 - TOTAL t*le iodine concentration in the reaction

mixture, b is the dilution factor (volume of sample divided by total

volume of dilution, usually 1/3), and e^^ is defined as the apparent J-2 extinction coefficient of iodine. From eqs. (14) and (13) it follows

that e^^ depends on the temperature of the diluted sample and its J-2

iodide concentration. For each run where any of these conditions changed,

a new value of f and hence of e^^ had to be calculated. When I2

precooled diluant was used, it was assumed that the temperature of the

dilution at the moment of taking the absorbance reading was the same

as that of the thermostat; if the diluant had been at room temperature,

the final temperature was estimated from the formula:

Tf = bTs + (l-b)Td (V-15)

where Ts is the temperature of the sample and T^ is the temperature of

the diluant (equal to the room temperature, constantly monitored with o

a thermometer hung above the bench, both in C). When deriving eq. (15)

equal heat capacities for the diluant and for the reaction mixture were

assumed. In the two cases it is also assumed that the dilution does

not warm up appreciably during the 1-1.5 minutes handling before reading

the absorbances.

82

V.4. Results and Discussion,

a) Extinction Coefficients.

The real extinction coefficients of reactants and products at

350 nm in 1 M KN03 are given in Table 3:

TABLE V-3. EXTINCTION COEFFICIENTS AT 350 nm IN 1 M KN03.

Species eT- 1 M KN03/(mol 1 1 cm 1) •1-3 Source

Fe(CN)6~ 304b p.w. 305 ref. (78) 318 ref. (79)

Fe(CN)e~ 175b ref. (78) 184 ref. (79)

I~ °b ref. (78) 0 ref. (79)

I2 600 p.w. 170 ref. (79)

i ; a 2.53 x 10* b p.w. 2.50 x 107 ref. (78) 2.63 x 107 ref. (80) 2.43 x 10 ref. (79)

p.w. = present work; a = with an excess of I b = value used in this work

The measured e* P P in 1 M KC^ (5°C, [l~] = 0.0167 M) was (2.29 + 0.02) x 104. J-2 —

Under these conditions f = 1.048. Therefore, from eq. (14)1

1 M KC€ _ app, 1 M KC/ ,, ,n , - n4 --1 - -1 e - = f eT = (2.40 + 0.02) x 10 mol 1 cm J-3 12 —

The values measured in this work agree with those determined by other 76-78 authors.

83

Our value for e was corrected for the absorbance of the I3 12

produced according to the following equilibria present in iodine

solution I

I2 + HoO — + HOI + H + Kx = 5.4 x 10~13 M (V-16)

I2 + > U K2 = 741 M"1 (V-17)

HOI ^ ^ H+ + Ol" K3 = 2 x 10~10 M (V-18)

+ HOI Kz, > 5.4 x lo" 4 M (V-19)

79 These equilibria are rapidly established. The equilibrium constants

quoted are at 25°C in water, except K2 which is in 1 M KN03 (Table 1).

The pH of a saturated I2 solution in 1 M KN03 was 5.09, well below

pH 6.72 of 1 M KNO3 alone. Using the equilibrium expressions for

equilibria (16) to (19), together with the balances of matter [H+] = [H+]0 + ([OH_]-[OH"]0) + 2[0I~] + [HOI] (V-20)

2[I2]o = 2[I2] + [I~] + 3[I3] + [HOI] + [0I_] + [H20I+]

(V-21)

and the electroneutrality expression

[H+] + [H20I+] = [OH ] + [f ] + [I3] + [01 ] (V-22)

and the ion product of water

[H+]O[0H"]o = [H+][0H_] = ^ (V-23)

(where [H+]0 and [OH ]0 are in the absence of iodine), one obtains

for a saturated I2 solution at ^ 20°C

[13 J = 3.4 x 10"6 M, [I~] = 4.8 x 10"6 M, [H+]0 = 5-1 x 10~6 M (V-24)

-4 The experimental solubility was 9.64 x 10 M which agrees with -3 77 1.053 x 10 M in 1 M HC/Oz, at the same temperature. The resulting

value of £ of 600 in Table 3 allows for the contribution to the -L 2

84

absorbance by I3. However, this may not be enough to obtain the true

e as the following equilibrium is also p r e s e n t ^ ' I J-2

30l\ ^ IO3 + 2I~ (V-25)

This contributes more I3 - forming iodide. The calculated pH for

1 M KN03 (-log[H ]0) is 5.3, markedly different from the experimental

value. This points to further reactions, besides reactions (16)

and (25) that push the pH to acid values.

It is difficult to say whether Reynolds' extinction coefficient

of 170 is closer to the " true" value than our result of 600, because

no explicit conditions are mentioned although pH < 4.8 is implied.

If the pH is acid enough then all of the I -forming equlibria are

repressed, including reaction (25). Luckily, however, the concentration

of free iodine is so small in our reaction mixtures than even an e I2

value as high as 600 would contribute less than 1% in the more dilute

iodide solution to the total absorbance of the samples. Therefore,

the actual value of £ is immaterial. J-2

b) Verification of the Value of K.

Because the values of K for our low temperatures had been obtained

from extrapolation of previous work^ in 1 M HC/Oz,, an attempt was

made to verify these values. Two hundred ml of 0.050 M KI solution

were electrolysed at 5°C, at 0.5 mA constant current in the manner

described, except that the WE platinum RDE was used at 500 rpm. Samples

of 5 ml were taken every 4 minutes and diluted with 10 ml of KN03

solution at room temperature. T,. was 15°C. was calculated from r 12

the change in absorbance between successive samples and from the number

of coulombs passed:

£app = 2F V. (A. - A. ) /I(t .-t. - K (V-26) la 3 3 3-1 J J-l

85

where V is the volume of the electrolyte at the moment of taking the

jth sample, I is the current and is the time interval between

successive samples. For eight samples, the results for T^ = 15°C,

[I~] = 0.0167 M were!

TABLE V-4

W M n4 app, --1 p -1 10 e r / mol -c cm I2 ' f - e ±3 12 K15°C/ mol"1 4 calc

0.5 2.39 + 0.06 1.059 + 0.003 1015 + 52

1.5 2.39 + 0.12 1.059 + 0.053 1015 + 910

The values were obtained from eq. (13). They are in reasonable

agreement with the value extrapolated from Katzin and Gebert's results

in Table 2, considering the large uncertainties involved due to the f

being close to unity, and the approximation incurred by using for conc.

KN03 values obtained in conc. HC Oz,. Table 4 suggests that K does not

vary much with [KN03].

c) Homogeneous Rate Under Various Conditions.

The results are summarised in Tables 5-9. The rates are expressed as

d [I2 ]/dt. The effect of reactants in the absence of the products was

measured as a test of the rate laws (5) and (7) and to obtain the rate

constant under our experimental conditions. The bracketted numbers in the

last column refer to the number of runs carried out.

86

TABLE V-5. EFFECT OF REACTANT AND SUPPORTING ELECTROLYTE

CONCENTRATIONS ON HOMOGENEOUS RATE, AT 5°C.

[KN03j/M [KC^J/M 103[Feic]/M IO3[KI]/M 109 v, /mol hom

0.5 0 1.0 50 0.361 + 0.006 (2)

1.0 0 1.0 50 0.65 + 0.02 (4)

2.0 1.22 (1)

3.0 1.95 + 0.20 (2)

1.0 0 1.0 70.7 1.20 + 0.01 (2)

0.95 100 2.46 (1)

0.85 200 16.5 + 0.02 (2)

0.75 300 41.8 + 1.5 (2)

1.5 0 1.0 50 0.849 + 0.11 (2)

0 1.0 1.0 50 1.12 + 0.002 (2) (2)

From the data in Table V-5 it can be calculated that the order in

[Feic] is 0.93 and in [l~] (below 0.1 M KI) 2.06. Figure 2 shows the

dependence on [KN03] which is close to first order below 1 M. This

agrees with the rate law in eq. (5). XXX —A — 2 2 —"1 The third order rate constant k is 2.50 x 10 mol € s at

o -4 5 C in 1 M KN03. In order to compare it with the value of 7.08 x 10

mol 3 A at 5°C for the fourth order rate constant, k1^, reported

by Majid and Howlett,^ one must divide by the free K+ concentration,

allowing for association between K+ and N03 (there is no need to consider

the association between K+ and Feic, since the concentration of the latter

is so small).

87

The association constant K is82b,C: 0.75 (18°C), 0.59 (25°C), ass 0.71 (25°C) and 0.56 (39°C), leading to K5 C ft 1.1 (+ 0.1) ^ mol"1 at ass — zero ionic streng-th . Therefore, one must include the activity coeffi-

cients appropriate to the concentrations involved. The molar concen-

trations, C (mol -6 were converted to molalities (mol Kg 1 of solvent) o 8 3a via the solution density, p, at 25 C according to the formula:

m = 1/(p/C-M) (V-27)

M is the molecular weight of the solute. The corresponding stoichio-

metric activity coefficients, (25°(^ are listed in Table 6.

TABLE V-6.

[KNO3J /mol / 1

25°C P /g cm 3

m /mol Kg 1

(25°C) Y+ 4

0.5 1.0279 0.512 0.545 0.297

1.0 1.0580 1.01*5 0.436 0.190

1.5 1.088 1.603 0.369 0.136

If we take the y+ at 25°C to be approximately applicable at 5°C, and

remembering that y+ = a f+ (a = degree of dissociation, and f+ = ionic

activity coefficient), the following table is obtained:

TABLE V-7.

[KNO3 /mol -C

2 Y, K + ass a [K+] /mol £ 1

104 k 1 1 1

, -2 -1 /M s

4 IV 10 k /m-3 -1 /M s

0.5 0.327 0.817 0.458 1.44 3.14

1.0 0.209 0.778 0.828 2.57 3.10

1.5 0.150 0.765 1.198 3.4 2.84

88

where the following expression has been used:

(l-o)/a(aC + 0.05) = f2 K (V-28a) + ass

or Y? K = (l-a)/f + 0.05/a) (V-28b) T A S O

where 0.05 refers to the molar K+ contributed by the KI. IV o -4 -3 -1 Thus, the mean value of k at 5 C is 3.03 x 10 M s , compared

-4 with Majid and Howlett's value (their Table 2) of(l/2)(7.1) x 10

-4 3.55 x 10 (their rate constants refer to Feoc formation, hence the 1/2 factor to convert them to iodine formation). However, the figures

IV in Table 7 suggest that k is not actually constant at the high ionic

strengths employed in this work, and that at the lower [K+] values IV -4 o used by Majid and Howlett our k is probably > 3 x 10 . At 25 C

k1^ = 8 . 7 x l 0 4 M ^ s 1 (using: k1*1 calculated from Table 5, K = ass 0.65, Y? K = 0.1235 for 1 M KN03; hence a = 0.870, and [K+] = + ass aC + 0.05 = 0.92). Majid and Howlett's is (from their Table 2)

(1/2)(18.8) x 10 4 = 9.4 x 10 Since their kIV are higher at their lower

ionic strengths, the disagreement is well within our uncertainty of

+ 4% (Table 5). o -9 -1 Our rate extrapolated to 0 C is 0.49 x 10 M s [Table 8 and

4 -9 eq. (29) J agrees with Spiro and Griffin's 0.51 x 10 in the same

conditions.

TABLE V-8. EFFECT OF TEMPERATURE ON HOMOGENEOUS RATE,

10~3 M Feic, 5 x 10~2 M KI, 1 M KN03.

T/°C 109vu /mol i hom - V 1 109 v [calc.eq.(29)]/mol ^ 1s 1

5 0.65 + 0.02 (4) 0.66 10 0.91 + 0.03 (4) 0.89 15 1.20 + 0.009 (4) 1.18 20 1.50 + 0.08 (4) 1.55 25 2.00 + 0.08 (4) 2.02 30 2.66 + 0.16 (4) 2.61

89

TABLE V-9. EFFECT OF INITIAL PRODUCT CONCENTRATION ON THE

HOMOGENEOUS RATE IN 1 M KN03, 5 °C.

103[Feic] /M

103[Feoc] /M

IO3[KI] /M

IO3[I2] /M

lO vi. /mol € 1s hom -1

1.0 0.005 50 0 0.62 (1) 0.010 0.72 (1) 0.020 0.65 (1) 0.050 0.68 + 0.12 (2) 0.100 0.57 (1) 0.500 0.48 (1) 1.000 0.25 (1)

1.0 0 50 0.012 0.67 (1) 0.020 0.69 (1) 0.040 0.80 (1) 0.100 0.58 (1)

1.5 0.4 50 0 0.817 (1) 2.0 1.09 + 0.1 (2) 1.0 0.4 60 0 0.713 + 0.005 (2)

70 0 1.054 + 0.011 (2) 1.0 0.010 50 0 1.99 + 0.17 (2)

0.100 1.95 (1) 1.000 1.47 (1)

The rate experiences a big boost when [Kl] > 0.1 M, although the

reaction order, w.r.t. I , settles at ^ 1.8. It is difficult to explain

this feature as Majid and Howlett did not observe such an effect under

similar experimental conditions.

The effect of temperature is shown in Table 8. The data are well

expressed by the Arrhenius expression, TTT _9 9 —1 ^

k /mol t s = 4.40 x 10 exp(-4625/T) (V-29) -1 with r = 0.997. The apparent activation energy E is 9.19 Kcal mol , Si

in fair agreement with Majid and Howlett's value of 8.4 Kcal mol \ and

90

-0.4 -0.2 0.0 0.2

Figure V - 2 iog[KN03i

Figure V-3

0.2 0.4 0.6 0.8 1

[ Feoc] / [ Feic ]

91

Hussain's value of 8.84 Kcal mol . The former did not correct their

data for the dissociation of I3, which tends to produce smaller apparent activation energies according to =

EaPP= E - AH(l-l/f) (V-30) a a

where f is given by equation (13), and AH is the

enthalpy change of (2). However, the decrease is marginal - 1 - 1 -

(of the order of 20-30 cal mol if K % 900 M and [I ] fy 0.2 M,

which fit typical Majid and Howlett's conditions). E contains too cL

the temperature variations of the other association equilibria: between

K + and N0 3 and K + and Feic; their contribution is bound to depend on

the concentration of the ionic species concerned, through expressions

like eq. (30). Thus, slight discrepancies between authors using

different total ionic concentrations are not surprising.

Table 9 shows the effect of the products. It should be mentioned

than values of [Feocj > 1 0 M are impractical because the rate becomes

-4

so small that it is difficult to measure. Also, [l 2J > 10 M cannot

be used because the large absorbances in both the sample and reference

cells of the spectrophotometer cause the absorbance pointer to wobble

markedly. Some of the data are plotted according to eq. (7) in Figure 3.

The points are scattered and they do not seem to correlate well

according to this plot. Conventional log-log plots were used instead.

For [Feoc] 1 5 x 10~ 5 M, [Feic] = 10~ 3 M, [l~] = 5 x 10~ 2 M, [KN0 3] = 1 M:

v, /mol f ' h ' 1 ^ (1.23 x 1 0 " 1 0 ) . [ F e o c ] " 0 , 1 7 (V-31) horn

u

In the presence of increasing concentrations of l 2 the rate seems to

increase at first and then to decrease. The mean rate of the four

o -9 -1 runs at 5 C is, however, only 0.68 x 10 M s , very close to

-9 -1 0.65 x 10 M s in the absence of this product. It seems reasonable

92

to conclude that iodine has no significant effect on the initial rate,

in agreement with the various mechanisms cited at the beginning of

this chapter.

The concentration dependence on the reactants in the presence of

-4 - -2 4 x 10 M Feoc were checked too. When [I ] = 5 x 10 M and [KN0 3] =

1 M at 5 °C:

v, /mol r 1 s" 1 = 5.47 x 10~ 9 [Feic] 1* 0 (V-32) hom

-3 In the presence of 10 M Feic, the dependence on C .- is!

v /mol r 1 ^ 1 = 6.17 x 10~ 7 [I~] 2' 4 (V-33) nom

This increase in the order w.r.t. iodide in the presence of Feoc is

not very significant, probably because of the lack of accuracy due to

the small rate values.

Because of the way in which rate-concentration data have been

expressed here in the presence of the products, the correlating equations

have been used in the next chapters for interpolation purposes but never

for extrapolations.

93

CHAPTER EIGHT

CATALYSIS ON PLATINUM (OXIDISED):

STUDIES IN THE PRESENCE 0? KN0 3

VI.1. Introduction.

The catalysis by platinum of reaction (1-1) has been studied by

1 4 69 85 4 several authors. ' ' ' Spiro and Griffin were the first to show

that catalysis proceeds by electron transfer through the metal, while

1 85

Spiro and Ravno and Hussain suggested diffusion-limited kinetics.

In this work the kinetics of the catalytic rate have been

measured for the first time, as well as the effects of stirring in

order to compare the experimental results with the theoretical predictions

in Chapter 2.

The work has been carried out on a rotating platinum disk which

allows precise control of the thickness of the diffusion layer by

controlling the gngular velocity of rotation (Chapter I V ) . The catalytic

rate JJ1 . i s reported as moles of iodine per unit time. Cat

VI.2. Materials and Methods.

The thermostat and experimental arrangement as well as the chemicals

have been discussed in Chapter V.

a) Platinum Rotating Disk Electrode.

The platinum RDE used in kinetic and electrochemical experiments

is depicted in Figure 1. It consisted of a mirror-polished circular

platinum plate of ^ 1 mm thickness and 11.2 cm 2 geometric surface area,

94

platinum brass former bakelite shaft

Figure V I -1

cri i IT 111111111»11 *»111111 iti 111111 i i rii f 111»11 r 11111111 IIWTTTTT

ii'iiiiiiiiiiiiiiiininmimmi miiiinnniiii

steel rod nylon screw

RE

RDE r

i k .

CE I Figure V 1 - 2

RDE E D

v^E CE

Figure VIII -3

95

soldered onto a trumpet-shaped brass former. The electrode was fixed

to the steel shaft of the rotating system by means of nylon screws.

Direct contact between the shaft and the brass former was avoided by

a bafcelite cylinder interposed between them. The non-platinum parts

of the electrode were covered with white radiator enamel (International),

and baked on in an oven for 2 hours at 100°C. The coat had to be

periodically removed with the enamel thinner as it tended to peel off

around the edges of the disk. Electrical contact was made through a stain-

less steel rod running down the hollow shaft and screwed into the back

of the disk. The top of the rod ended in a mercury-filled teflon cup

into which a lead fitted with a platinum coiled wire was dipped. The

rod was wraped in 2702 P.V.C. adhesive tape (Rotunda Ltd., Denton,

Manchester). When rotating, the edge of the disk oscillated horizontally

+ 0 . 3 mm around a central position; a slight up and down movement at

the edge could also be observed. This indicated that the disk was not

perfectly horizontal and that it had a slight excentricity. The motor

driving the disk was a motor generator type 126/54451 (Newton Brothers

Ltd., Derby). The speed could be controlled within + 1% of the fixed

speed with a Motor Controller, type MC43 (Servomex Controls, Ltd.); it

was checked with Stroboscopic disks permanently attached to the shaft,

using ordinary neon lamps as a source or with a universal counter, number

835 (Racal Communications, Ltd., Bracknell, Berks.), attached to a

Racal tachometer, type MA38. The maximum speed tolerated by the motor

generator was 6000 rpm. In practice, however, funnelling and swirling

of the solution around the disk limited the speed to 2000 rpm. Above

this limit bubbles tended to be sucked in. The theoretical limit for

the onset of turbulence for a critical Reynolds number of 10"* [eq. (V-4)]

is over 5000 rpm for a disk of our dimensions. It is possible that the

lateral motion of the RDE contributed to this limitation of the speed.

96

Runs at 2000 rpm were carried out in vessels of 10 cm inner diameter

instead of the ordinary 7.5 cm vessel because funnelling tended to

decrease in this large vessel.

b) Pre-Conditioning.

Prior to catalytic or electrochemical experiments the electrode

was electrochemically pre-conditioned to obtain an oxidised surface.

This was done in 1 M H 2S0*, prepared in doubly distilled water (distilled

the second time from an alkaline permanganate solution in an all glass

still). Oxygen-free nitrogen was passed through the solution in the pre-

conditioning cell, shown in Figure 2, for 10 minutes. The pre-conditioning

was carried out at the same temperature as would be used in subsequent

kinetic or catalytic work. The counter electrode was a 8.5 cm x 8.5 cm

platinum foil placed at the bottom of the RDE compartment. The reference

electrode was always an EIL calomel reference electrode, number 1320,

3.8 M KC/. However, at 5°C at which most of the work was carried out,

some KC€ precipitated; before using it at higher temperatures, enough

solid K.C€ Aristar grade (BDH Chemicals Ltd.) was added to the electrode

in order to keep it saturated. When not in use, it was stored in

saturated KC€ and placed inside the thermostat. All the potentials

quoted are vs. this electrode, unless otherwise specified. To facilitate

comparisons, a table of the potential of the saturated calomel electrode

(SCE) vs. the standard hydrogen electrode (SHE), taken from the book by

Ives and Janz , is given in Table 1.

TABLE VI-1.

T/°C 0 5 10 15 20 25 30

E/V 0.2602 0.2572 a 0.2541 0.2509 a

0.2477 0.2444 a 0.2411

a • interpolated value

97

The electrodes were connected to the terminals of the potentio-

stat (TR70/2A, Chemical Electronics Co., Durham); the potential

between the RE and WE was monitored with a Hewlett Packard digital

voltmeter model 3440A, with a high gain auto range unit, model 3443A.

The current could be calculated from the voltage drop across a 100 fi

(5%) resistor placed across the counting resistor terminal of the

potentiostat.

The pre-conditioning potential sequence applied is shown in Table

2, the electrolyte being de-oxygenated 1 M H 2 S 0 ^ .

TABLE VI-2

E vs. SCE/V Time o)/rpm

1.560 10 s 500

0.960 40 s 500

-0.162 3 s 0

1.400 10 min 0

The timing was checked with a chronometer (English Clock Systems) which

permitted 1 second accuracy. It was occasionally checked with a Rone

chronometer (0.25 accuracy). These usually agreed within 0.5ff. The

86 87 sequence is similar to Gilroy's as recommended by Gilman : at

1.560 V adsorbed organic impurities are supposed to be oxidised, and

desorbed at 0.960 V; at -0.162 V the surface is rendered free of oxides,

87

a process completed during the first 10 ms according to Gilman, but

does not lead to H-atom deposition; the growth of the oxide is achieved

at 1.400 V, without (or with little) oxygen evolution. At this 88

potential only a thin layer of superficial a-oxide is formed. It

is a fast process, requiring a few tens of ms to complete a monolayer

98

of oxygen. Rotation during the first two steps should help to

carry away the oxidation products. During the last two steps the

disk was kept motionless to dimish deposition of cations which might

be present as impurities. The RDE was then removed from the cell,

rinsed with doubly distilled water and spun at high speed in the air

for a few seconds. It was left in the air while arrangements for

the subsequent run were being carried out, usually 10 minutes.

The electrode was used as found at the beginning of this work.

It was never repolished, although it was occasionally wiped with

Kleenex paper to remove white specks that accumulated with time. Its

performance, as measured by the rate of the catalytic reaction, remained

remarkably constant during the course of this work 3 years), after

85

and before cleaning off the specks. By contrast, Hussain reports

that his platinum foil catalyst showed a marked decrease in performance

with time which he attributes to organic growths on the catalyst surface

as revealed by electron micrographs. His pre-treatment consisted in

washing the catalyst with concentrated HC^; it was stored in acidified

distilled water. The state of this surface is therefore unknown

though it may well have been in a more reduced form. It would appear

that the difference in sensitivity towards contamination probably rests

on the pre-conditioning procedures.

Repeated oxidation and reduction of platinum leads to roughening 89

of the surface, according to Biegler. In our case, repeated pre-

conditioning would then have led to increased catalytic rates. A

balance between progressive contamination and progressive roughening

might have been achieved, thus keeping the apparent catalyst performance

unaltered.

99

c) Steady State Current-Voltage Curves.

Steady state current-voltage curves were carried out with the cell

shown in Figure 3, the same solution being used in both compartments.

Oxygen-free nitrogen was passed through the solution for about ten

minutes before recording the curve, which was carried out with the

TR70/2A potentiostat, capable of a minimum of 1 yA. The current was

monitored by the voltage drop across a 400 (0.1%) resistor, type

RBB1 (Croydon Precision Instruments Co.) connected to the counting

resistor terminal of the potentiostat. The applied potentials were

monitored within 0.1 mV with a Hewlett Packard digital voltmeter.

Prior to the run, the solution was electrolysed with the aid of an

auxiliary WE (see Section V.2, d) to obtain either 2 yM ferrocyanide

or 1 yM I 3 .

The solutions were prepared according to the same general procedure

as used for the homogeneous runs. They were initially made up in doubly

distilled water, but later ordinary distilled water was used since the

same results were obtained.

The current became steady a few seconds after setting the potential

between the RDE and RE, after which it decreased gradually by ca. 0.1%

every minute or so, probably due to the accumulation of the product and

the consumption of the reactant. The formal potential of the ferricyanide

solutions tended to be 20-30 mV less positive after completing a curve,

and that of the iodide solution 30-40 mV more positive; also, the

absorbance at 421 nm of a ferricyanide solution indicated some 6%

decrease in which compared favourably with 6.9% calculated by

Faraday's Law from the currents at each potential and the estimated

time spent at each (typically, less than 1 minute) which also indicates

that not all of the product is reoxidised at the counter electrode.

100

Luckily, the curves were very reproducible, at least in the mixture

potential region, and relatively independent of the period spent at

each potential (see Figure 4). ^reproducibilities tended to show

up at higher currents, and in this case probably contain IR drop errors

due to uncertainty in the position of the Luggin capillary.

The limiting current densities Ly of ferr(i/o)cyanide, iodide

and iodine as a function of Cj at a constant u> = 500 rpm at 5°C in

1 M K N 0 3 , were measured in separate runs with a view to determining

the mass transport rate constants k^. The only precautions worthwhile

-3 -mentioning is that L^- was measured in the range of 10 M < [I ] <

-3 47 4 x 10 M in order to avoid formation of thick layers of solid iodine.

From previous experience, the approximate position of the current

plateaus were known, so that the i-E curves were started at or very close

to the Ly region, and E advanced in ca. 10 mV steps. The current

readings were taken quickly. The whole run took no more than 2-|- - 3

minutes. The results are listed in Table 3. The k^' values were obtained

from the slopes of the least squares fitting of the Lj vs. CQ data.

Using the Levich equation, the resulting ratios

are 0.868 and 1.71, respectively (at 5 °C in 1 M KN0 3). The corresponding

values reported at 25°C are 0.71 for ferr(i/o)cyanide in 1 M K C / , 9 0 and

23 91 2 in KI for iodine couple. '

From the Stokes-Einstein equation , eq. (III-l), values of D^.n/T

92

were calculated using the values of ky in Table 3 and A = 11.2 c m 2 .

The values were well within the range of values reported in the

literature.

101

< E

few sees at each point

w X * x * * *

2 min at each point

X*3

f **

400 300 200 100

E I mV(SCE)

0 -100

usual E m

0.001M Feic, 1 M KNO^, 500rpm, 5'C

Figure V I - U

Figure VIII -3

102

TABLE VI-3. LIMITING CURRENTS IN 1 M K N 0 3 , 500 RPM, 5°C, ON 11.2 cm 2

PLATINUM RDE.

(mol / 1 ) 1 0 3 L^/A kj/A M 1 Residual Current at

c-,- = 0 b ( 1 0 3 A)

10 3 [Feic] 1.0 2.74

(+ equimolar 2.0 5.34 Feoc)

3.0 8.07 2.665 0.053

10 3 [Feoc] 1.0 2.44

(+ equimolar 2.0 4.87 Feic)

3.0 7.29 2.425 0.017

10 3 [KI] l.Olf 4.98

(no iodine 1.07 5.08 present)

2.05 9.73

3.34 15.8 4.717 0.059

5.114 a 23.8 a

7.879 a 36.4 a

10 3 [I 2] 0.4715 3.19

(+ 0.1 M KJ) 0.9326 6.25

1.399 9.30 6.588 0.092

Not considered for calculating Jc -; Calculated from intercepts.

103

d) E.m.f. Measurements.

The e.m.f. of the cell

Pt | I~, I3, KN0 3|| KNO3, Fe(CN)6~» F e ( C N ) | P t (VI-1)

was measured at several temperatures. Each half cell was a 50 ml beaker

filled with the corresponding solution, immersed in the thermostat. The

bridge was an Agar gel (see Section V.2.d). The concentrations used

were [Feic] = [Feoc] = 2 x 10~ 3 M; [l~] = [I3]1" = 4 x 10~ 2 M, [KN0 3]

was 0.5, 1 or 1.5 M. The I 3 was generated by passing 1.050 mA during

- 2

30 minutes through 150 ml of 4 x 10 KI in 1 M KN0 3 to give 6.528 x

10 ^ M I 2 (net). The e.m.f. of each half cell was measured against a

SCE always kept in the right hand side cell. The temperature was

raised from 5° to 30°C in 5°C steps. Readings were taken when the

e.m.f. did not appear to vary in a 15 minute period by more than 0.1 mV.

e) Catalytic Runs.

The basic arrangement is shown in Figure 5. The preparation of the

solutions has been described in Section V.2.a. The preconditioned

electrode was normally immersed in the KI solution, and so was the SCE.

The solution was allowed to equilibrate thermally for 10 min while the

disk rotated. The reaction was started by addition of the ferricyanide

solution. The sampling procedure has already been discussed. Aliquots

were taken every 4 minutes, 8 samples per run. The values were

monitored with the DVM (Hewlett Packard). Addition of the products

was done according to Section (V.2.d.).

f) Treatment of Kinetic Data.

The absorbances were given the same t r e a t m e n t as described in

Section (V.3). Because of eq. (II-8) v must change appreciably when C A U

the volume of the reaction mixture changes by 40 ml due to sampling.

104

Following the definitions of Section (II.2.a.), let us assume that

V h m a n c ^ u c a t a r e c o n s t a n t . The concentration of I 3 in each successive

sample C x , C 2> ••• of size v ml is then:

C l - C ° + V h o m A t l + " I f

C > - C l + V h o m A t l +

(VI-2a)

(VI-2b)

and for the N-th sampleI

Au C„ = C„ , + v, At +

cat At.

N N-l hom N V0-(N-l)v N

where Aty is the time interval between sample j-1 and j.

On addition, we have for the N-th sample:

(VI-3)

^N V h o m ~N t - C 0 + A ucaj.S N

(VI-4)

where N

S = I At /[V 0-(j-l)v] j-1 3

N

t = I At , to = 0 j = l J

(VI-5a)

(VI-5b)

Therefore a plot of C - v, t„ vs. S„ should produce a straight line from N hom N N

whose slope the initial catalytic rate v c a t can be calculated according

to eq. (II-8). In practice, some of the resulting plots had slight down-

ward curvatures, thus suggesting that uCaf decreased with time. The data

were therefore fitted by least squares to a second degree polynominal

(see Appendix 2) of the form:

CN " *hom

fcN

= C o + A u« t

SN +

(VI-6)

The catalytic rate is reported as u* in moles of iodine per second C 3 X

( ucat

= A uc a H

105

VI.3. Results and Discussion.

a) Comparison of Kinetic and Electrochemical Experiments.

Figure 6 shows typical kinetic plots according to eq. (4). The

lines usually do not cross the origin due to the uncertainty of the

absorbance of the reference solution. This should not affect the slope

at t = 0. Figure 7 shows typical I-E curves of ferricyanide and iodide.

Their intercept denotes the mixture current and potential on the

assumption of additivity. The value of the catalytic rate (in mA) at

the catalyst potential E obtained under the same experimental conditions Call

is shown as a filled circle in Figure 7. It should coincide with the

intersection point within experimental error if the electrochemical

mechanism is followed. The closeness of the two points in many runs is

taken as evidence in favour of the hypothesis, thus confirming earlier

4

results by Spiro and Griffin. The results of these comparative

experiments are shown in Table 4. They prove that within experimental

error the catalysis proceeds by electron transfer through the metal.

TABLE IV-4. KINETIC AND ELECTROCHEMICAL RUNS

o 10 M Feic, 0.05 M KI, 1 M KN0 3, 5°C

0)

/rpm

10 9 u' E cat cat

/mol s~l /mV

109 i /2F E

m ^ m /mol s /mV

100

500

1.12 + 0.07 (3) 293 + 1 (3)

2.48 + 0.03 (5) 295 + 1 (5)

1.17 + 0.01 (2) 293 + 0.5 (2)

2.36 + 0.07 (5) 294 + 0.4 (5)

Number of runs are in brackets. Appended figures (+) are standard

deviations of the mean.

106

0 8 0 160

S t l /mini"1

50mM K I , 1 M K N 0 3 , 500 rpm, 5'C

Figure V 1-6

107

260 2ft 0 300 320

108

During the kinetic runs the catalyst potential reached quite stable

values almost immediately after completing addition of the ferricyanide

solution; it fell by about 1 mV during the 30 minutes of reaction.

It was always very close to the final equilibrium potential.

_ The dependence of u' on w is shown in the plot of 1/u' vs. oo 2

cat Cat

(Figure 8) and Table 5. The line passes through the origin, which

according to eq. (11-36) indicates that the reaction at the surface is

very fast and therefore probably in equilibrium at the catalyst surface.

This is borne out by the constancy of E with co, according to eq. cat

(11-30). It is worth checking the reversibility of the electrochemical

couples.

TABLE VI-5. DEPENDENCE OF CATALYTIC RATE AND POTENTIAL ON u>

10~ 3 M Feic, 5 x 10~ 2 M KI, 1 M K N 0 3 , 5 °C.

o)/rpm 10 9 u' /mol s 1

cat E /mV cat

100 1.12 + 0.07 (3) 293 + 1 (3)

200 1.56 + 0.05 (2) 293 ± 5 (2)

300 2.06 293

500 2.48 + 0.03 (5) 295 ± 1 (5)

1000 3.74 293

2000 5.42 + 0.3 (2) 292 ± 1 (2)

From eq. (11-30), assuming that [Feoc] = [ l 3 ] = 0 and that i/L^ « 1

for Feic and I , it follows that the two i-E curves are described by!

i = 1

+ exp [f(E-E%) ] ( V I _ y )

1 LFeic k„ [Feic]

. Feoc and

1 ^ 3 + exp[-2f (E-Ei)] (VI-8)

i 1 7 k - [ l " ] 3

1 i 3

109

0.001 M Feic, 0.05 M K I , 1 M KN03 , 5'C

LU 1/1

296

.3 292

1

0.5

0.02 0.04 0.06

1 //u> irpm)

0.08 0.1

Figure V 1-8

110

Therefore a plot of ln(l/i - v s * E f°r Feic/Feoc couple,

and of ln(l/i - 3/L^.-) vs. E for the I /I 3 couple, should furnish

straight lines, as shown in Figure 9 at 100 rpm and 500 rpm.

The slopes are close to the expected 41.7 V 1 for Feic/Feoc and

-83.4 V 1 for I /l 3, and they pass very close to the calculated values

-ln(k„ [Feic ]) and -ln(k -[l ] 3) when E = E°., which are shown as reoc I 3 j

squares on the curves. Near the formal potentials there is a marked

deviation from linearity, probably because the initial small amount of

product cannot be neglected at these low currents. The mixture potential

luckily lies well inside the unequivocal reversible region, and the

catalytic rate may be described by the model in Section II.2.c. The

magnitudes of the kinetic parameters to be expected in several situations

are shown in Table 6, according to Table II-l.

TABLE VI-6. EXPECTED KINETIC PARAMETERS FOR THE CATALYSED REACTION

1-1 UNDER TOTAL MASS TRANSPORT CONTROL.

Reaction Order w.r.t. Calculated rate

Condition Reactants Products . J> constant x 10

Fe(CN) l, I Fe(CN)s~ I3 (5°C, 500 rpm,

1 M KN0 3)

No added product

2/3 1 0 0 5.70 a mol s" 1

Added Fe (CN) 6

2 3 -2 0 1.17 mol s 1

Added Is

1 3/2 0 -1/2 2.33 mol s" 1

a From W (eq. II-36a).

I l l

100 rpm

o—o 500 rpm

• : expected value of ln(1/I - G)

LD

0.001 M Feic, 2|iM Feoc 0.05 M K I , 1|iM I~ 1 M KN03

500rpm 5'C <

112

b) Theoretical Calculation., of Catalytic Rates. The catalytic rate at 5°C, 500 rpm, and in 1 M KN0 3 was calculated

from several concentrations of reactants and products, by solving

eq. (11-31) for i and then converting to units of u' : the value of m cat

i was used to calculate E , or E , from eq. (II-30b). The k . used m m cat j

were those in Table 3: the E?, those in Table 13. Solution of eq. J

(11-31) was accomplished numerically either by the Newton-Raphson

93

method or by successive partitioning of the interval to which the

solution belonged (Appendix 3). Identical numerical results were obtained

by both methods.

c) Effect of Reactant Concentration.

Table 7 summarises these effects on u 1 and E . cat cat

TABLE VI-7. EFFECT OF CHANGES IN THE REACTANT CONCENTRATION

1 M K N 0 3 , a) = 500 rpm, 5°C.

1 0 3 [Feic] 10 3 [KI] 10 9 u' _ cat

/mol •€ 1

^cat /mV

/M /M exp. calc. exp. calc.

0.2 50 0.71 0.78 279 280

0.5 1.45 1.52 286 288

1.0 2.48 2.49 295 294

2.0 3.72 4.05 299 300

5.0 6.85 7.65 307 307

1.0 30 1.45 1.57 306 307

50 2.48 2.49 295 294

80 3.68 3.70 283 282

150 5.82 5.89 263 265

300 5.80 8.74 245 244

113

The agreement between the experimental and the calculated value is good.

The slightly larger calculated u' values could indicate a certain cat

amount of interference between the couples.

It is important to calculate the reaction orders in [Feic] and [i ].

-3 -2 At 10 M Feic and 5 x 10 M KI the ratio 2F u' /L. is 0.18 for

cat 3

Feic and 0.002 for iodide. Thus, in eq. (II-36b) the L^.- term may be

neglected, but not the term, and to obtain the reaction order

the ln(l/u' - 4F/3L„ . ) should be plotted vs. In C.. From the cat Feic r j

resulting slopes the order w.r.t. Feic is 0.66 + 0.02,

and w.r.t. I , 1 . 0 2 + 0 . 0 1 , in excellent agreement with expectations.

85 — Hussain too found an order of 0.7 w.r.t. Feic and 1 w.r.t. I . The

—6 — 6 rate constant of 5.24 x 10 from the Feic plot, and of 5.03 x 10

from the I plot are somewhat lower than the predicted values in Table 6.

The dependence of E on In C. is shown in Figure 10. According to cat J eqs. (11-41) the slopes should be -24.0 mV and +7.99 mV for 3E /91n[l~]

cat

and 8E /81n[Feic], respectively. The actual values of -23.2 mV and Cat

8.25 mV agree reasonably well considering the approximations involved

in these equations. At constant [Feic], the ratio 2F u' . becomes cat Feic

more favourable for u' to be represented by eq. (11-41) at the lowest C A U

[I ] values, while at constant[I ] high [Feic] should be preferred.

This is why the lines in Figure 10 are biased towards the experimental

points more likely to meet this condition.

d) Effect of High Fe(CN)s~ Concentration.

High Feoc concentrations should have important effects on the kinetics,

as summarised in Table 6. The approximations in the theory require that

i m or be very small so that significant experimental uncertainties

result. Disagreement between the expected and the experimental reaction

orders may be a result of these uncertainties or of the fact that a value

114

1 M K N 0 3 , BOOrpm, 5°C

Figure VI-10

E I mV (SCE) Figure V1-11

115

of u ; a t low enough has not been reached. Therefore numerical calculations

of u' are useful to check that the reaction follows the predicted cat behaviour. The results are in Table 8. The order in Feic appears

TABLE VI-8. EFFECT OF ADDED Fe(CN)g~ ON CATALYTIC RATE

5°C, 500 rpm, 1 M K N 0 3 .

Concentration x 10 3/(M) u' X cat

10 9/(mol s 1 ) E „ cat

/(mV) E l e V / m V

Fe(CN)6 I Fe(CN)e~ exp. calc. exp. calc.

0.5 50 0.4 0.124 0.200 263 264 265

0.7 0.248 0.361 270 271 273

1.0 0.552 0.650 278 278 282

1.5 1.00 1.19 285 285 292

2.0 1.59 1.76 290 290 298

1.0 30 0.4 0.109 0.179 280 281 282

32 0.145 0.214 279 280

34 0.267 0.252 280 280

37 0.321 0.313 279 280

40 0.338 0.382 280 279

50 0.552 0.650 278 278

60 0.876 0.962 277 276

70 1.17 1.30 274 274

1.0 50 0.001 2.39 2.48 294 294 425

0.01 2.31 2.42 293 294 370

0.1 1.71 1.82 290 290 315

0.2 1.16 1.30 286 286 286

0.4 0.552 9.651 278 278 278 0.6 0.265 0.352 271 270 270 1.0 0.046 0.140 259 259 260

116

to be ^ 1.8 and that in I ^ 2 . 8 over the concentration range studied.

These values are certainly far away from the orders in the absence of

products. The orders approach the predicted values of 2 and 3,

respectively (Table 6). That they do not quite reach these values may

be due to the ratios 2F u 1 L_ not being small enough and to the cat Feoc

experimental uncertainty as becomes smaller and smaller. The order

in Feoc is ^ -2.5, in excess of the expected value of -2, again, probably

because of experimental uncertainty. The order using the last two lines

in Table 8 is -1.8 in that concentration region. The feature of note

in Table 8 is the generally good agreement between

the experimental rates and potentials, and the calculated values, in

these extreme conditions.

rev

The reversible (formal) potential of the Feic/Feoc couple, E 2 ,

has been calculated from the Nernst equation and the E° values in

Section VI.3.g. Table 8 shows that as [Feoc] increases, the catalyst rev potential remains close to E 2 during the reaction, because the i-E

curve for this couple becomes much steeper, as shown in Figure 11 ,

rev so that E must lie very close to E 2

m

e) Effect of High I 2 Concentration.

The concentration range that can be explored with I 2 is limited

because of the high optical absorbance in both the sample and reference

cells due to the background I3• This makes the spectrophotometer

readings highly unstable because the small absorbance increase due to

the I 3 produced by the reaction depends on the small difference of two

large quantities. The results are shown in Table 9. The agreement

with theory is fair.

As explained in Chapter II, the effect of the products on the rate

has a thermodynamic origin! the equilibrium at the catalyst surface is

117

TABLE VI-9. EFFECT OF HIGH ADDED IODINE CONCENTRATION

" 3 o 10 M Feic, 1 M KN03, 5 C, 500 rpm.

i o 3 [ k i ]

/M

i o 3 [ I 2 ]

/M

10 9 u' _ cat

exp.

/mol s 1

calc.

E _ cat

exp.

/mV

calc.

^rev , TT Ei /mV

(calc.)

37 0.01 1.62 1.90 303 302 281

0.03 1.53 1.65 305 305 294

0.05 1.09 1.52 306 308 300

50 0.01 2.39 2.40 294 295 270

0.03 2.08 2.23 297 297 283

0.05 1.96 2.09 298 299 289

displaced towards the reactant side according to the principle of

Le Chatelier, thereby reducing the concentration gradient across the

diffusion layer. This decreases the rate-controlling fluxes of the

various species.

f) Effect of [KNO3].

Changing the supporting electrolyte concentration affects several

parameters. Among these are the viscosity and density of the solution;

the diffusion coefficients depend on the ionic strength and on the

viscosity [eq.(III-l)]; the formal potentials E° depend on ionic strength

too. The change in u' on [KN0 3] is shown in Table 10, as well as the cat

difference E 2 - E ? .

118

TABLE VI-10. EFFECT OF [KN0 3]. _ o

10 M Feic, 0.05 M KI, 500 rpm, 5°C.

[KN0 3] 9

10* u' _ cat

Ex e°2 E 2 - E ° a 10" 8 2 F W _ 1 K 2 / 3

/M /mol s~l / v / v / V /mol s

0.5 1.84 0.2951 0.2430 -0.0523 1.16

1.0 2.48 0.3000 0.2598 -0.0404 1.15

1.5 2.79 0.2980 0.2638 -0.0343 1.19

Directly measured difference.

The calculation in the last column is an attempt to correlate the

value of u' with the change in E 2-E? or its equivalent equilibrium Cat

constant, K, equal to exp[2F(E°2-E°i)/RT]. The quantity W 1 is, according

to eq. (II-36b):

2F/W = 1/u' _ - 4F/3L.„ . (VI-9) cat Feic

-1 2/3

Thus, by eq. (II-36a) the product W K should remain constant if all

of the change in u^ ^ is due to changes in E2-EI. The constancy of the

figures in the last column (+ 2%) supports this view, that variations

in the equilibrium constant override all of the rheological variations

when the concentration of the supporting electrolyte is changed. 85

The increase of u' with increasing [KN0 s] was noted by Hussain cat

too, who attributed it to increased ion pairing between K+ and Feic

that facilitates electron transfer at the catalyst to the K^-Feic complex.

This is a basically correct interpretation. The changes in E2 towards

more positive values support it.

119

g) Effect of Temperature.

This is shown in Table 11, which reveals that the rate decreases

as the temperature is increased. From the Arrhenius plot

an apparent activation energy of -4.05 Kcal mol 1 is obtained by

least squares (the homogeneous reaction has an activation energy of

TABLE VI-11. EFFECT OF TEMPERATURE ON THE CATALYTIC RATE 10~ 3 M Feic,

- 2 5 x 10 M KI, 1 M K N 0 3 , 500 rpm.

T/°C 9

u' x 10 cat /mol s

5 2.48

15 1.86

20 1.73

30 1.35

+9.20 Kcal mol 1 (Section IV. 4.c)) . This surprising negative value can

be explained in terms of the total mass transport control model in

Chapter II. In effect, from the definition of apparent activation energy:

E = -R" ^ = - R3 L N ( K L F ^ E ° C ) . 2F 8[(ES-E»,)/TI ( „ _ 1 0 )

a 3(1/T) 9(1/T) 3 3(1/T)

where only the temperature-dependent terms have been included. From the

definition of k . in eq. (11-13)1 J

i 1/3 2/3 -p.2/9 „4/9 -1/6 / U T i n k T - k_, a DT- D_ v (VI-11) I3 Feoc I3 Feoc

where again temperature-independent terms have been left out. Since values

of the diffusion coefficients are not available in 1 M K N 0 3 , it is

convenient to introduce the Stokes-Einstein equation:

D = kT/6irnr (VI-12)

120

where r is the radius of the diffusing molecule. Although this equation

is unlikely to hold quantitatively for the linear I 3 ion, it is not

unreasonable to assume that over a short temperature range D a T/r).

Thus, eq. (10) becomes!

,8 ln[v 1 / 6 ( T / n ) 2 / 3 3 2F 3(E°2-E?)/T E = - R ^ ^ i - ^ — » - y (VI-13) a 3 ( 1 / T ) 3 3(1/T)

Thus the activation energy is composed of the activation energy for

diffusion, expressed by the first differential term, and by the change

in the standard enthalpy of the reaction, AH 0. This follows from the

Gibbs-Helmholtz equation, taking n = 1:

AH 0 = [3(AG°/T)1

= -F

[ 3 (1/T) J \

3(ES-E;)/T

3(1/T) (VI-14)

The transport term was evaluated from tabulated data. Viscosities

of 101.1 g KN0 3 in 1000 g H 2 0 (9.183% by weight) were obtained from

94 Landolt-Bornstein. The density of this solution was interpolated from

83a

the data of 8% and 10% solution from International Critical Tables.

With these data, at 10°C a 9.183% KN0 3 solution is ^ 0.965 M, which is

close to our experimental conditions. The resulting data are displayed

in Table 12. From the corresponding Arrhenius plot an

activation energy, of + 3.63 Kcal mol ^ is obtained.

TABLE VI-12. VARIATION OF n AND p WITH TEMPERATURE FOR 0.965 M K N 0 3 .

T /K

P /g cm 3 ,

71 -1 -1

/g cm s

-9 2 -2 -1/2 X°2 V S

V3 / 2

/ K g cm s

273.15 1.0624 0.01624 2.288

283.15 1.0603 0.01217 5.053

303.15 1.0536 0.007925 16.871

121

The temperature variation of thermodynamic term is shown in Table

13. Figure 12 shows the corresponding plot of (E°-E?)/T vs. 1/T, from

which it is possible to calculate:its contribution to Eg'as -7.72 Kcal mol

TABLE VI-13. EFFECT OF TEMPERATURE ON e.m.f. s 2 x 10~ 3 M Feic,

2 x 10~ 3 M Feoc, 4 x 10~ 2 M KI, 6.4 x 10~ 7 M I 3 , 1 M K N 0 3 .

T/°C Ei/V E2/V e.m.f. a/V e.m.f. b/V

5 0.3000 0.2598 -0.0404 -0.0402

10 0.3021 0.2514 -0.0508 -0.0507

15 0.3031 0.2425 -0.0606 -0.0606

20 0.3039 0.2333 -0.0706 -0.0706

25 0.3043 0.2244 -0.0800 -0.0799

30 0.3044 0.2156 -0.0889 -0.0888

a b From direct measurement; Calculated from E 2-E?

Thus:

E = -7.72 Kcal mol" 1 + 3 . 6 3 Kcal mol" 1 = -4.09 Kcal mol" 1

a

very close to the experimental value of -4.05 Kcal mol

By inspection of the rate constant in the absence of products in

Table II-l and of the form of eq. (13), the apparent activation energy

may be expressed as!

E = (v E°Xl + V , E^ed2)<J> + <f>AH° (VI-15) a ox, d red 2 d

Assuming that the diffusion activation energies of ox t and red 2 are

equal(=E d):

Ea = Ed + <f)AH° (VI-16)

The energy diagram in Figure 13 represents the path of the reaction

along the 'reaction coordinate*. The first step, bringing the reactants

from the bulk of the solution to the catalytic surface, requires almost

122

- u r

* -1 .8 >

UJ

- 2 . 2

-2.6

-3 .0 L

3.2 3.3 3A 3.5 3.6

Figure V1-12

10/ T C K )

Figure VI-13

b = bulk of solution

0 = catalyst surface

reaction coordinate

123

no energy expenditure, because of the a s s u m p t i o n i /L. ^ 0 (j = ® J

reactants) which makes C a & ^>ulk ^ ^ surface the reactants u reactants

products are formed very quickly, liberating an amount (|>AH0 calories

<Kf

on assuming equilibrium concentrations. Therefore, as far^the catalyst

is concerned, the reaction rate is instantaneous. However, transport

of products to the bulk phase does require energy, and since it involves

the highest barrier in the sequence, controls the rate. Increasing

the temperature shifts the equilibrium to the reactant side, and

although it is easier now for the products to climb the diffusion

barrier, there is less of them at the surface so that the overall balance

is unfavourable to the rate.

VI.4. Conclusions.

The results in the previous section show that reaction (1-1) is in

equilibrium at the surface of oxidised platinum, the reaction being

controlled by the rate of mass transport across the diffusion layer.

The fact that the partial electrochemical charge transfer reactions:

Fe(CN) + e" *Fe(CN)Jf (VI-7a)

3/2 i" > 1/2 1~3 + e~ (VI-7b)

are also in equilibrium at the mixture potential is a strong indication

that equilibrium of the overall reaction takes place by electron transfer

between the reactants across the metal catalyst. The fact that neither

33,4

of the participants of the reaction is adsorbed on oxidised platinum,

seems to rule out any mechanism other than charge transfer through the

metal. Furthermore, this absence of adsorption renders more probable

the assumption of undisturbed overlap of the i-E curves. Therefore,

each substance reacts according to their individual mechanisms of

electron transfer.

124

32-34 38 95 96 The Feic/Feoc system has been studied on platinum ' ' '

_ 34,36,37,97 , . -.. . 98 ,. gold, mercury and thallium-amalgam, sodium-tungsten

99 100 bronzes, and on the soft metals bismuth, lead and cadmium. Once

mass transport-free data are obtained, the overall picture, especially

on platinum and gold is that of a basically simple electron transfer.

Tafel plots tend to be linear, giving anodic and cathodic transfer

32-34 coefficients close to 0.5 the reduction reaction is first order

32-34 36 on [Feic], and the oxidation one is first order on [Feoc]. The

33 97 differential capacitance of platinum and gold is independent of the

concentration of the electroactive species, which rules out physical

17g

adsorption. & There is no evidence that the primary coordination shell

(the cyanide shell) is in any way altered during the reaction, a

characteristic it shaves with MnO A/MnO£ and Mo(CN)s /Mo(CN)s ^ ^

systems. In this respect, their electrodic behaviour is no different

from that in the homogeneous electron exchange of these s y s t e m s , ^ ^

processes called "outer sphere reactions"

Because of its large radius [3.51A the centre of the hydrated

Feic or Feoc anion does not coincide with the outer Helmholtz plane,

OHP, which is the locus of the centres of the fully hydrated cations

of the supporting electrolyte in contact with the electrode surface 1 1^ + 0 107

(the Stokes radius of the K ion is 1.3A ). Thus, the centre of o

these anions is ^ 2A inside the diffuse double layer, as has been shown

by Frumkin.9 8

Double layer effects play an important role in the reduction of Feic.

Electrostatic repulsion between the negatively charged electrode and the

highly charged anion (Frumkin effect, Chapter I), especially in dilute

solutions of the base electrolyte, leads to a considerable drop in the

current on bismuth, lead and cadmium electrodes at potentials more 98 100

negative than the potential of zero charge (Epzc). ' The magnitudes

125

of these effects follow the sequence Bi > Pb > Cd, in accord with the

trend in the negativity of their Epzcl Bi < Pb < Cd. The Frumkin

effect must surely be a universal phenomenon, but its influence is

often masked by other phenomena like H deposition and oxide formation

especially on platinum.^

However, the authors in references 98 and 100, have not considered

the possible effects of ion pair formation between the Feic/Feoc

35 species and the cations from the base electrolyte, which also shifts

the standard reduction potential of the couple towards more positive

36 values. It has been suggested, that the enhanced kinetics are not

so much due to more favourable E?, but to a different mechanism by J

which the activated complex is formed by collision of a cation with

the already formed ion pair. This explains the observed first order

dependence of the current on the cation concentration. The activation

energy itself is independent of the concentration of the supporting

36

electrolyte. The effect of the cation is not merely to reduce cou-

lombic repulsion with the electrode, but to provide a new pathway for

the electron transfer through a bridge between the electrode and the

reacting anion. This process has been treated t h e o r e t i c a l l y , ^ ^ 15 19 20 by an extension of current quantum theories of charge transfer, ' '

and found to be more likely than direct non-bridged, electron transfer.

97

A detailed study conducted on gold electrodes has led to the conclusion

that the reduction of Feic proceeds by the electron hopping first from

the metal to the bridge, and then from here to the anion. Since this 19

transfer is radiationless its occurrence depends on equalisation of

the electron energy levels of the ions by a favourable random fluctuation

on the solvent polarisation around the ions, at which point the electron 19 may tunnel between the degenerate energy levels in the activated complex.

126

Theoretical treatment of these effects, including bridging by a cation,

leads to the result that the experimental transfer coefficient a exp

from Tafel plots corrected for every possible kind of extraneous

effects is given by1"*:

a = 0.5 + (E-Er.eV)F/2\ (VI-8) exp j

where X is the energy that would be required to change the solvent

of configuration from that of the reactants to thatjLthe products, while

keeping the reactant nuclei at their equilibrium positions. Its value

106 has been estimated at ^ 1.2 eV. From the dependence of a on the

exp

potential, values of 0 . 4 5 , ^ 0.31, and 0.83 eV have been found.

At low concentrations of supporting electrolyte the double layer effect

of Frumkin would appear as well. The I /I 3 system has not been studied

to an extent comparable to Feic/Feoc. Mechanistic knowledge is still

at a macroscopic stage and there is no agreement between the authors

as to its course (cf. Chapter III). This is because the relatively

complicated events of bond forming/breaking, and of charge transfer

with possible adsorption of I or I 2 on the electrode surface.

It has been reported that the exchange current density for iodide

oxidation on previously oxidised platinum exhibits a 1/2 order dependence

111 on the concentration of the K 2 S 0 A base electrolyte, which again has

been attributed to Frumkin effects. However, the analysis of the

experimental data is based on the assumption of irreversible adsorption

of iodide, which is unjustified as iodine species do not adsorb 45

irreversibly on platinum. Whatever the mechanisms of the Feic/Feoc

and I /I 3 charge transfers at the oxidised platinum surface, our

evidence shows that they occur side by side in the mixed solution.

127

Rigorously speaking, however, one cannot deduce the mechanism of

the reaction from the fact that equilibrium has been reached at the

surface: for a given mass transport regime, the rate will be the same

regardless of the mechanism (or mechanisms) leading to surface equili-

brium. However, we have been able to show that the experimental (i , m

E ) values coincide with the (2F u' , E ) values, thus ruling out m cat cat

mechanisms other than electrochemical.

Another point concerns the species involved in the establishment

of the formal potential and/or diffusion overpotential in the case of

the Feic/Feic couple, since the cation-paired species must participate

in the electron transfer too. Considering only association with one

cation, K + in this case, two equilibria are possible, with association

constants, K. and K : 1 o

+ K. K + Fe(CN)1 v

1 ^ KFe(CN)I (VI-9a)

4- _ K K + Fe(CN) 6 9 ^ i n w r w ) ; (VI-9b)

Therefore, there are two simultaneous electrochemical equilibria!

Fe(CN) + e " ^ = z± F e ( C N ) 6 _ , E° (Vl-lOa)

KFe(CN) + e \ s K F e ( C N ) s ~ , E° (Vl-lOb)

These equilibria occur both in open circuit conditions (thus giving rise

to the formal potentials of the couples) or in steady state current flow.

In any case, only one potential is possible at the electrode. Then!

E = E° + (1/f) l4Feic]/[Feoc]) (Vl-lla)

= E° + (1/f) lnjt KFeic ] /[KFeoc ]j (Vl-llb)

where the E° s are the standard equilibrium potentials of the couple

concerned. The concentrations refer to those of the actual ionic

128

constituents-. Either of eqs. (11) may be used to formulate the mixture

potential in eq. (II-30b). From equilibria (9) it is found that

[Feic] = [Feic] 0/(1 + K [K +]) (VI-12a)

[Feoc] = [Feoc] 0/(l + K 0 [ K+ ] ) (VI-12b)

or that

[KFeic] = [Feic] 0/(1 + 1/K.[K +]) (VI-13a) I

[KFeoc] = [Feoc] 0/(1 + 1/K 0[K+]) (VI-13b)

The subindexed brackets refer to the overall Feic or Feoc concentration.

Thus, whether one uses eq. (11a) in conjunction with eqs. (12) or eq.

(lib) in conjunction with eqs. (13), the mixture potential depends on the

overall concentration of Feic or Feoc.

129

CHAPTER SEVEN

CATALYSIS ON PLATINUM (REDUCED).

VII.1. Introduction.

The state of the electrode surface usually has noticeable

consequences on electrode kinetics. Therefore it is important to

examine this factor in an electrochemical catalytic mechanism.

The catalysis of reaction (1-1) on reduced (i.e., oxide-free)

platinum is reported in this chapter.

VII.2. Experimental.

a) The chemicals and the experimental procedure were the same as in

Chapters V and VI. All the experiments were carried out in doubly

distilled water at 5°C. The catalytic runs were made either in the

presence of 1 M KN0 3 or 1 M K C A

b) Pre-Conditioning Procedures.

All the solutions employed were de-aerated with nitrogen. Once

reduced (i.e., after step c in the following tables) the electrode was

usually rinsed with doubly distilled water, spun in the air at high

speed and left in it for ca. 10 minutes while the subsequent run was

being prepared. The different procedures listed below were carried

out in the sequence a, b, c, etc. In between the steps, the electrode

was left on open circuit.

130

CAT (H 2S0 a)

< Step Supporting

Electrolyte E vs. SCE /V

Time GO/rpm

a 1 M H 2 S 0 4 1.560 5 s 500

b 1 M H2S0z, 0.960 40 s 500

c 1 M H2S0z» -0.162 3 s 0

CAT (KCO

Step Supporting Electrolyte

E vs. SCE /V

Time to/rpm

a 1 M K.C€ 1.560 5 s 500

b 1 M KC€ 0.960 40 s 500

c 1 M KC-f <-0.6 ^ 3 min 0

33

Step c in CAT (KCO is similar to that used by Daum and Enke in their

study of the Feic/Feoc couple on platinum. Steps " a " and " b " were

added in order to free the electrode of organic impurities. As this 114

may cause dissolution of the metal, the oxidation steps were later

carried out in 1 M H2S0A, and the final reduction step in 1 M KC/

(see following table).

CAT ( H 2 S 0 m KCl)

Step Supporting Electrolyte

E vs. SCE /V

Time co/rpm

a 1 M H 2S0* 1.560 5 s 500

b 1 M H 2S0* 0.960 40 s 500

c 1 M KC-e -0.600 15 min 0

131

After step b in the CAT (H2S0z,, Y&-C) procedure, the electrode was

rinsed and spun in the air.

CAT (H2S0/,, KC/)/KI.

The CAT ( H 2 S 0 4 , K C O procedure was first performed. Then enough

_2

solid KI was added to the 1 M Y£€ on open circuit to make a 5 x 10 M

solution, while the electrode rotated at 500 rpm for 10 minutes.

CAT ( H 2 S O a > K C Q / K I / R M .

After the CAT ( H 2 S 0 A , KC/)/KI preparation the electrode was taken

out, rinsed, and immersed for 10 min at 500 rpm in a reaction mixture

-3 -2 containing 10 M Feic, 5 x 10 M KI and 1 M KN0 3 which had been

prepared some 4 hours earlier.

c) Cyclic Voltammograms (CV).

Cyclic voltammograms were obtained by connecting a Chemical

Electronics linear sweep generator LSI to the external input of the

Chemical Electronics TR70/2A potentiostat. The CVs were recorded on a

Hewlett-Packard 7035B X-Y recorder. Its X-terminals were connected

directly to the RE and WE terminals of the potentiostat; the Y-terminals

(for current recording) were connected across a 100 ft (5%) counting

resistor (Figure IV-7a). The recorder settings were chosen so that

its input resistance was larger than 0.1 M ft (the input resistance

for each setting was listed in the instrument manual). This would have

produced a maximum current drain of 15 yA at the largest potential

differences between WE and RE (1.5 V) . Since the currents obtained

are in the mA range, the error produced by this drain is not serious.

The CVs reported here are interpreted mainly in a qualitative way.

132

VII.3. Results and Discussion.

a) State of the Surface Following Pre-conditioning.

Figure 1 is a CV of the RDE in 1 M H 2 S O A , o) = 200 rpm, at 5°C, at

a sweep speed of 28.5 mV s " 1 , between 1.560 V and -0.150 V. The

electrode had been preoxidised according to the procedure outlined in

_2 Table VI-2, rinsed and immersed in a 5 x 10 M KI in 1 M KC^ for

5 minutes, and rinsed again. The CV started in the cathodic direction

to

(starting point marked " 5 " ) from OCV, and shows an oxide reduction

peak at 0.4 V as would be expected from a pre-oxidised electrode (cf.

Figure III-l). This peak shifts to 0.43 V in subsequent sweeps (marked

" 2" and " 3" ) that reach the 1.560 V anodic limit. (Other features

of the CV have been described in Chapter III, but our aim here is to

show what happens to the oxide peak following pre-conditioning). Shifts

in the oxide reduction peak towards more irreversible values (i.e.,

further away from the oxide formation region) as the positive limit

of the sweep becomes more anodic have been attributed to re-arrangement 29 112

of the oxide layer. 9 Progressive irreversibility with time at

113

constant potential has been observed too, and explained as strengthening

of the oxide. Thus, the oxide formed according to Table VI-2 remains

stable and attached to the surface in all the handlings preceding the

catalytic run, and it is not altered either by contact with KI + KC/

solutions.

Figure 2 shows the CV of the electrode preconditioned according to

CAT (H2SO4), rinsed, immersed in 1 M KC^ without KI at OCV, and rinsed

again. The conditions of the CV carried out in 1 M H2S0*» are the same

as in Figure 1. As expected, the first cathodic sweep lacks the oxide

reduction peak at 0.4 V (although it reappears in subsequent sweeps at

*0pen circuit voltage

133

Figure VIII -3

134

Figure VI1-2

135

0.42 V); the horizontal trace appearing in its stead might be due

to adsorbed atmospheric oxygen, reducible impurities from the KC-^

that remained adsorbed all through, ditto from the H 2 S 0 ^ , or the

double layer charging current. In any case, this graph confirms the

oxide-freeing result of the CAT (H2S0/») preconditioning.

Figure 3 shows the CV of the RDE in 1 M KC^ oxidised according

to Table VI-2 and rinsed before the CV. The CV was carried out at

0) = 0 rpm, at 31 mV s " 1 , between -0.850 and +0.210 V. The first

cathodic sweep, started from OCV (marked 11 S" ) produces a large oxide

reduction peak at -0.3 V , which disappears from the subsequent sweep

since it was not allowed to reach oxide-forming potentials. The marked

cathodic peak at -0.85 V is probably due to hydrogen evolution. The

preceding H-adsorption/desorption peaks in the -0.6 to -0.8 V region are

not as resolved as in H 2S0*, (Figures 1 and 2) . Resolvability of this

112 region is connected with the cleanliness of the solution. This

suggests that the 1 M KC/ solution is a rather " dirty" one. The

0.7 V shift of the CV w.r.t. those obtained in H 2S0<, may be due to a

combination of factors such as shift of the formal potentials of the

oxide reduction and hydrogen evolution reactions due to change in pH

—6

(RT/F In 10 = -0.35 V), kinetic effects and possible blockage of the

surface by adsorbed impurities. What Figure 3 shows clearly is that the

oxide is reduced in 1 M KC^ well before -0.600 V, the potential used in

the pre-conditioning procedures for the reduction step.

b) Kinetic and Electrochemical Runs.

Table 1 shows the catalytic rates and the equivalent quantities

obtained from the crossing points of the steady state current-voltage

curves.

Figure V

II-3

137

TABLE VII-1. CATALYTIC AND ELECTROCHEMICAL RUNS

Q O

10 M Feic, 5 x 10 M KI, 5°C, 500 rpm

1 M KN0 3 (unless stated otherwise).

Preconditioning 1 0 9 u ' „ cat

/mol s ^

E ^ cat

/mV

i /2F m

/mol s ^

Ervi

/mV

CAT (H2S0Z.) 1.83 291 2.36 293

CAT (HaSOj 1.66 a 290 2.33 b 292

CAT (H 2S0„) 1.47 a 287 2.33° 292 C

CAT (KC-0 1.89 290

CAT (H 2S0„, K C O d 2.37 290 2.82 293

CAT (H 2S0*, KC^)/KI 1.35 287 2.10 290

CAT ( H 2 S 0 a , K C O / K I / R M 0.76 280 1.38 286

a -6 -7

In the presence of 2 x 10 M Feoc and 1.2 x 10 M I 2 .

k i-E curve of I in the presence of 1.2 x 10 ^ M I 2

C Duplicate of previous entry

^ Kinetic and electrochemical runs in 1 M KC/. RDE not exposed

to air after preconditioning.

These results are illustrated in Figures 4 and 5 where both the

catalytic points (E , u' 2F) and the i-E curves are shown. They cat cat

do not agree with each other, the catalytic rates being consistently

lower than the "mixture current" rates. Moreover, the catalytic

rates obtained with CAT (H2S0A) are clearly irreproducible.

138

A :CAT(H2SOJ

B C//A B : C A T ( H 2 S 0 4 ' K C l ) / K I

c .cat(h2so4jkcd/ki/rm

D :CAT(KCl)

0 :oxidized

• : catalytic points

cf. table V11-1 tor conditions

Feic / Feoc ' f/1"

0

270 280 290 300 310

E I mV (SCE) 320 330

Figure VI1-4

1 r

0.8

0.6

0.4

Feic /Feoc A H C

139

0.2

250 300

E / mV (SCE)

350

CAK^SO KCL), 0.001 M Feic/2|IM Feoc, 0.05 M KI/1[JLM I~ , 1 M KCL, 500rpm,5°C

Figure V11 - 5

140

Oxygen adsorption as a cause for the discrepancy between catalytic

and electrochemical runs was ruled out by carrying them out in 1 M KC/

without removing the RDE from the preconditioning cell. Enough solid

salts of reactants were added to the KC/ to attain the desired final

concentrations after preconditioning. Nitrogen was continuously passed.

For this purpose, the calomel RE was placed inside the RDE compartment

of the cell used (Figure VI-2) while the large platinum CE was rolled

and squeezed inside the compartment normally occupied by the RE. The

results are given in Table 1 and in Figure 5. The remaining preconditioning

procedures, CAT (H 2S0*, K C O /KI and CAT (H2S0/», K C O /KI/RM, were devised

to test any effect of the reactants and products on the state of the

surface just before the runs.

The disagreement between the two sets of experiments is probably

a result of iodide and iodine adsorption which blocks the surface to

the approach of Feic during the reaction although the latter still

proceeds electrochemically. In effect, iodide adsorbs on reduced

i . . . 45,115,116 platinum as iodine according to:

H I I I

I + —Pt—Pt— + H 2 0 > —Pt—Pt— + OH (VII-1) I I I I

Iodine atoms cover 1 x 10 9 mol cm

2 H 5 , 1 1 6 c o m p a r e < j ^ t h a surface

—9 - 117 concentration of platinum atoms of 2 x 10 mol cm

2. Iodine in

-9 — _ 45 solution also adsorbs, covering 2 x 10 mol cm . Adsorbed iodine

is electrochemically inactive, but it allows reversible redox processes

- - 115 of soluble I /l 3 and Br /Br 2. It blocks the oxidation of impurities

below ca. 0.3 V (SCE) in neutral aqueous solutions."'"'^ As shown in

Figure 4, iodine adsorbed prior to the i-E curves inhibits the reduction

of Feic but does not affect the oxidation of iodide. Ferricyanide

reduction curves not involving previous contact with iodide-containing

solutions a«*e identical to those obtained on the oxidised electrode

141

(dashed curves on Figure 4), at which the Feic/Feoc couple is in

equilibrium. This also happens to the I oxidation curve. Therefore,

the coincidence of the catalytic points with the iodide oxidation

curve clearly shows that the reaction is still proceeding through the

electrochemical mechanism. However, under these conditions the I /l 3

couple remains in equilibrium during the reaction, while the Feic/Feoc

couple is being interfered with by adsorbed iodine.

It is interesting to note that the catalytic rate is always lower

than the corresponding rate from the i-E curves. This is because of

further adsorption of iodine from the reaction mixture during the

reaction. It is assumed that the H-co-adsorbed layer in eq. (1) formed

during iodide-containing preconditionings is destroyed by aerial

oxidation, because the electrode is exposed to air just before the

reaction [except in the CAT (H2SO*,, KC/) procedure]. This also explains

why the CAT ( H 2 S 0 4 , KC/)/KI/RM surface produces lower catalytic rates

than the CAT (H 2SO*, KC^)/KI one. In other words, undisturbed overlap

of the individual i-E curves does not hold true in the mix^ed solution

on reduced platinum. The system investigated thus provides clear

evidence of the failure in certain cases of the additivity hypothesis

of Wagner and Traud.

c) Verification of Iodine Adsorption.

This was carried out by first subjecting the electrode either to

oxidising preconditioning (Table VI-2) or to the reducing one according

to CAT (H2SOI») . The electrode was rinsed and immersed at open circuit

_2

in a non-deaerated 1 M KC^ solution containing also 5 x 10 M KI or

saturated with iodine. It was then rinsed and a CV was performed at 5°C

i n 1 M H2S0Z, .

142

- 2 Figure 6 is a typical CV obtained when 5 x 10 KI was present

during the immersion step. The absence of H-adsorption/desorption

peaks in the first scan indicates the presence of adsorbed iodine

115 118

which block the metal surface for hydrogen atoms. ' Two anodic

peaks (A and B) that appear at 1.2 V and 1.28 V (SCE) respectively

are near the reported value of ca. 1.1 V (SCE) at ca. 25°C at which

adsorbed iodine is oxidised to I0 3 H 5 , 1 1 8 .

I + 3 H 2 0 > IO3 + 6 H + + 5e~ (VII-2)

A single peak is reported by these a u t h o r s 1 1 ^ ' 1 1 8 who preadsorbed their

iodine usually from H 2S0*, or HC^Oz, solutions. When iodine was pre-

119

adsorbed in the presence of KC-^, two peaks appear at 1 and 1.1 V

(Na-calomel electrode) respectively. The latter appears where these

and other 1 1"* 1 1 8 authors have reported iodine oxidation [eq. (2) ]; C€

ion alone adsorbed only provokes inhibition of monolayer oxide

formation at 1.05 V (SHE) without apparently suffering faradaic reactions

25

up to 1.4 V (SHE) (See Figure 2). Thus, peak B is probably due to

adsorbed iodine oxidation. The nature of peak A is unclear. Identical

results are obtained if the sweep is started in the anodic direction.

In Figure 6, once the surface material has been oxidised, subsequent

sweeps (marked " 2" and " 3" ) are similar to that in Figure 1. The

combined charge enclosed by the two peaks (obtained by weighing the

cut-out traces, having estimated the base line by eye) is 11 + 2 mC, -9

from six independent CVs, which gives an apparent coverage of 2 x 10

mol cm 2 , assuming that all of the charge is due to reaction (2), and

taking the real area of the electrode as 11.2 c m 2 . If iodine is present

143

Figure V

I1-6

144

instead of iodide during the immersion step, the peak currents are

1.4 and 2.2 mA for A and B, respectively (their usual height is ca.

1.7 mA each, measured from the estimated base line). The total charge

remains close to 11 m C . Exposure to 0.1 M KI0 3 in 1 M H 2 S 0 A (60 min.)

-3

or to 10 M Feic (30 min) after the immersion step (and rinsing),

and prior to the CV (and rinsing), also produced a " shift" of charge

from peak A to peak B (the relative value of the peak current was very

similar to the I 2 case), while the total charge was close to 11 mC.

These results are difficult to explain because of the mainly

qualitative approach of these experiments. The salts used were of

AnalaR grade which is not suitable for experiments involving adsorption.

The use of KC^ as a base electrolyte is not convenient because of

simultaneous adsorption of C/ and I ions, which further complicates

the interpretation of the results. At least it seems clear by comparison

of CVs in Figure 6 and 2 that iodide (as iodine) adsorbs on a reduced

platinum electrode.

VII.4. Conclusions.

The catalytic rate on reduced platinum, under a variety of pre-

conditioning procedures, proceeds by electron transfer through the

catalyst. The mechanism is of a mixed type not considered in Chapter II,

by which the I /I 3 is totally mass transport controlled during the

reaction, while the Feic/Feoc is not, because adsorbed iodine blocks

the catalyst to this couple. The i-E curves are thus not additive,

failing to comply with Wagner and Traud's hypothesis.

145

Quantitative study of this system requires knowledge of the

electrode kinetics of both couples on the covered electrode. Adsorption

of iodine would be expected to cause major differences to the I /I 3

couple between reduced and oxidised electrodes. The effects are not

observable because the rate constants are large enough in both cases

for the system to remain at equilibrium. Some studies on this theme

are described in Chapter III. The precise role of the irreversibly

adsorbed iodine (adsorbability towards I or I 3 or I 2 , and towards

cations, structure, bonding to the metal, effect on the potential

profile across the double layer, electrical conductivity, etc.) is worth

studying, particularly because of its impressive effects on Feic

reduction. Irreversibly adsorbed iodine affects the oxidation of

115 119—121

Pt(II) and Sb(III) complexes ' which has been adscribed to

desorption of less tightly bound anions , thus making the potential at

the outer Helmholtz plane less negative. 1 1"* This would explain the

enhancement in the oxidation of negatively charged platinum complexes 115 1 and Sb(III) complexes, and the lack of effect on neutral complexes. '

Ferricyanide is a negatively charged reactant and one would expect its

reduction to be enhanced by iodine-induced double layer effects. The

fact that just the opposite happens indicates that some other factors

are at play. The extent to which cations (i.e., K + ) can act as a bridge

between the iodine layer and the K+Feic ion pairs might be one of

these (Section VI.4).

146

CHAPTER EIGHT

CATALYSIS ON PLATINUM (OXIDISED)I

STUDIES IN THE PRESENCE OF KCl

VIII.1. Introduction.

This chapter is devoted to the effect of a different supporting

electrolyte, KC/, on the catalytic rate on oxidised platinum. Consid-

ering that the couples involved in reaction (1-1) are in equilibrium

at the oxidised platinum surface in 1 M KN0 3 (Chapter VI), it is

almost certain that they will continue to be so in KC/, and thus the

effects of the latter on the rate are bound to be modest.

VIII.2. Experimental.

a) The source of the chemicals has been mentioned in Chapter V. The

supporting electrolyte during the catalytic runs was 1 M KC/. The

runs and the i-E curves were carried out according to the procedure

described in Chapter VI. Oxidation of the platinum RDE was accomplished

according to Table VI-2. All experiments were carried out in doubly

distilled water.

b) Electrolyses.

Electrolyses at constant current (typically, at 0.5 mA, 5°C, on

0.250/ of 0.05 M KI, plus supporting electrolyte, for 30-60 minutes,

while the RDE was at 500 rpm) were carried out with the arrangement

described in Chapter V. They were intended to study the I /I 3 couple;

147

therefore the platinum RDE duly preoxidised was used. Electrolyses

at constant potential [293.0 mV (SCE)] of 0.05 M KI solution either

in 1 M KC/ or in 1 M K N 0 3 , at 5°C, 500 rpm, were carried out in the

three-compartment cell in Figure 1. The solution composition w a s the

same in all compartments, but the WE one contained exactly 0.250 ^ of

solution.

During both constant current and constant potential electrolyses,

the formation of iodine was followed spectrophotometrically at 350 nm,

from 1:3 dilutions with supporting electrolyte of 5 ml samples with-

drawn every 4 minutes from the WE compartment.

c) Chemical Analysis of Solutions After Electrolysis.

After electrolysis at constant current, the solution was treated

with sulphuric acid, after extraction of the iodine formed in the

electrolysis, to try to detect oxidising compounds such at 10 or I0 3

that might have been formed.

About 100 ml of the electrolysed solution were shaken in a

separating funnel with seven 15 ml portions of CC^z» in order to extract

the iodine formed. The absorbance at 350 nm of samples of the aqueous

extract, diluted 1:3 with the supporting electrolyte ranged from 0.004

to 0.078, compared with 1.1 of similar dilutions of the unextracted

solution.

Nitrogen was passed through the aqueous extract for 10 minutes to

evaporate the CC/<,. Then 1 ml of 1 M H 2 S 0 A was added to 10 ml of

extract, and the absorbance at 350 nm read. This reading had to be

corrected for the absorbance of the residual tri-iodide, taking into

account the dilution factors. The resulting absorbance ranged from

148

r

E T

RDE r ^

CE .z

Figure V I I 1 - 1

o—o kinetic

•—• electrochemical

1//u) (rpm)

0.001 M Feic, 0.05 M K I , 1 M K C l , 5°C

Figure V111-2

149

0.048 to 0.214. A control test was made on a 0.05 M KI + 1 M KC^

solution that had not been electrolysed. No significant increase

in the absorbance was produced upon mixing with the acid.

d) Treatment of Electrolyses Data.

In order to compare the total number of moles of iodine (as coulombs)

present in the solution at any time t., Q.(t.), (j = number of sample) 3 A 3

obtained from the absorbance, A^, of diluted samples, with the charge

passed by the current and that still remains in the solution, Q (t.), ^ 3

allowance must be made for the " withdrawal" of charge due to the

prece ding j-1 aliquots of size, v. Q.(t.) is simply given by: w A j

Q,(t.) = 2FA.(Vo - (j - l)v)/h.€ e * P P (VIII-1) A J J 1 2

The subindex, A, indicates that the calculation is based on absorbance

readings. Now, let AQ_., the charge passed by the current, I, during

the time interval between two successive samples, j-1 and j,

be defined by:

A Q j = " ' J

I dt (VIII-2)

V i

The relation between Q (t.) and Q r(t._ n) is then*. ^ J C j ±

Qc(t.) = AQ. + F j ^ t t j ^ ) (VIII-3)

The subindex C, indicates that Q is based on the current passed.

is defined as:

F = 1 - v/[V 0-(j-l)v] (VIII-4)

150

It represents the fraction of Q (t._,) retained in the remaining C j 1

solution volume after removal of the j-th sample. Application of

eq. (2) to successive values of Q (t.) gives! ^ 3

W - ^ + ( V l ) A V l + ( F i - l F j - 2 ) A Q j - 2 + +

+ ( F j _ 1 F 1 ) A Q 1 (VIII-5)

Since the F. are always less than unity, Q p at the end of the electrolysis 3 k

will be always smaller than the corresponding value obtained by

integration of the current alone (from t = 0 to t = t^) if samples

have been taken. It is important to observe that the analysis of Q u

is not based on any mechanistic or stoichiometric assumption. It

applies to any system other than I /I 2. The main requirement is that

the current be known as a function of time in order to obtain the AQ.s 3

in eq. (2). If all of the current is used to convert I into I 2 or I 3 ,

then Q.(t.) = Q (t.). If substances other than I 2 are formed, then A 3 ^ J

Q.(t.) < Q (t.), provided that they do not absorb at 350 nm. For the A 3 ^ 3

special case in which only one unknown substance is formed in quantity

of m ^ mols, the number of equivalents, n, may be calculated as!

n = ( Q C " Q A ) /F m

x (VIII-6)

VIII.3. Results and Discussion,

a) Preliminary Results.

The catalytic rates at 5°C at several rotation speeds from kinetic

runs and from the mixture current of i-E curves-of the reactants are

.summarised in Table 1. The fact that the plots of 1/u' and of 2F/i cat m

_JL_ vs. a) 2 in Figure 2 give straight lines which in each case pass very

close to the origin, and the independence of E and E on GO, indicate cat m

that the reaction is completely mass-transport controlled and is

therefore in equilibrium at the surface as with KN0 3 (Chapters II and VI).

151

TABLE VIII.1. CATALYTIC RATE FROM KINETIC AND ELECTROCHEMICAL EXPERIMENTS

ON OXIDISED PLATINUM 3 l o " 3 M Feic, 0.05 MKI, 1 M KC/, 5°C.

03/rpm 1 0 9

/mol

i u „ cat - 1

s

E /mV cat

i o 9

/mol

i /2F m -1

s

E /mV m

200 1 , 5 3 + 0 . 1 5 (2) 293 (1) 1 . 7 6 + 0 . 0 3 (2) 293 + 1 (2)

300 1 . 9 7 (1) 2 . 1 7 + 0 . 0 2 (2) 293 + 0 . 5 (2)

400 2 . 0 9 + 0 . 2 1 (2) 293 + 0 (2) 2 . 4 1 + 0 . 0 7 (2) 294 + 1 (2)

500 2 . 5 6 + 0 . 0 8 (3) 294 + 0 . 5 (2) 2 . 7 4 + 0 . 0 7 (6) 293 + 1 (6)

1000 3 . 6 1 (1) 293 (1) 3 . 9 0 + 0 . 0 1 (2) 293 + 1 (2)

2000 5 . 0 8 (1) 292 (1) 5 . 4 7 + 0 . 2 2 (2) 293 + 0.6 (2)

Numbers in parentheses indicate number of runs. Appended + figures

are the standard deviations.

The plots of i-E data for each reactant according to eq. ( 1 - 4 3 )

(allowing for the presence of 4 yM Feoc in the Feic curve, and of

2 yM I 2 in the I curve) give straight lines (Figure 3 ) . The L_.s were

calculated using the k^ s previously obtained in 1 M K N 0 3 (Table V I - 3 ) ,

although they are likely to differ in 1 M KC/ because k_. depends on

the viscosity and density of the solution which depend on the nature

of the electrolyte. The D_.s depend too on this factor. The expected

slopes are 8 3 . 5 V _ 1 for I~/ll and 4 1 . 7 v " 1 for Feic/Feoc. The

observed slopes, marked on the figure are close to the expected ones,

except for I /I 3 at 2000 rpm, which indicates a deviation from the

reversible behaviour. The expected value at E = is marked as a

heavy dot. The agreement is fair considering that they too are likely

to be different in 1 M K.C€. The currents due to Feic or to I at

152

0.001 M Feic 4 |iM Feoc

0.05 M KI 2 |1 M I"

1 M KCl

500 rpm

5°C

o o 200 rpm

• • 2000 rpm

—i 28

•

- 4 r

m i i.

- 6

- 8

-10 -

- 10 u

280 300

E / m V ( S C E )

Figure VIII - 3

2.8

2.0

1.2

10.4

2.0

1.2

10.4

'-0.4

340 -"-OA

153

500 rpm are consistently 15% higher in 1 M KC/ than in 1 M KN03 at -3

the same potential, all other conditions being the same (10 M Feic

or 0.05 M KI, 5°C), probably reflecting the different E? s and

rheological values.

Although Ecat and E^ agree within 1 mV, the catalytic rates are always

lower than the ones of i-E origin. The mean value of the difference

(which appears to be independent of GO) is 2.7 x 10 mol s \ outside

the experimental uncertainty. The catalytic points (E , 2Fuf ) are C a L C a t

shown in Figure 4 together with the sections of the appropriate i-E

curves. The catalytic points do not lie close to any of the curves

in a regular way (but tend to be close to the I /I3 curves, except

at 500 rpm, where they are closer to the Feic/Feoc curve). Any such

tendency is probably smothered by the experimental uncertainty in the

catalytic and in the electrochemical data because the departures from

the intersections are not large enough, unlike the situation encountered

with reduced platinum (Chapter VII).

Initial efforts to find a reason for this discrepancy were

directed towards finding some faulty points of technique. It was possible

for example, that in KC^ solution products from the counter electrode

might have reached the RDE and affected the current since both electrodes

were in the same compartment (Figure VI-3). To test this, i-E curves

were carried out in a three-compartment cell (Figure 1) in which glass

frits separated neighbouring compartments. No difference was observed

in the curves obtained in this cell. Also, a catalytic run was carried

out in the large compartment of the two compartment cell (Figure VI-3)

(the RE compartment contained ca. 0.05 M KI in 1 M KC€) at 500 rpm,

but no difference was found with respect to the ordinary single

scales and conditions as in fig. V I -7 except that 1M KCl was used instead of KNO

E

Figure V I I I-4

12

11

10

0 20 CO 60 80

time / min

1 M KCl, 500 rpm, 5#C

Figure V I I I - 5

155

compartment reaction vessel. The dilution factor, b, in eq. (V-15)

was checked by weighing 3 samples of 10 ml 1 M KC/ at room temperature

(measured with a grade B 10 ml volumetric pipette), and their increase

in weight due to a father 5 ml aliquot (grade B 5 ml volumetric 4 pipette). It was found that b was equal to 1/3 within 1 part in 10 .

Loss of iodine to the air from the reaction mixture was tested by —6

periodically sampling a solution of 0.0424 M KI, ca. 12 x 10 M I2,

1.04 M KC/, at 5°C, and stirred with the RDE at 500 rpm. According

to Figure 5, no significant amounts of iodine were lost to the air

in a 80 minute period.

The background currents-of 1 M KC^ at 500 rpm, 5°C, in the absence

of Feic and I are shown in Figure 6, together with the i-E curves of

Feic and I . The background contribution around the mixture potential

(293 mV) is negligible, even if the KC/ solution had not been purged

of oxygen. The i-E curves of Feic/Feoc and I /l3 had been obtained

with purged solutions.

As a test for the presence of irreversibly adsorbed iodine,

the i-E curve of Feic/Feoc was obtained at 5°C, 500 rpm, 1 M KC/, on

a pre-oxidised electrode which had been put in contact with 0.05 M KI

in 1 M KCtf after preconditioning but before the i-E curve (thoroughly

rinsed between stages). This was indistinguishable from the ones

obtained with the electrode subject to the usual oxidising pre-

treatment.

Thus, the above tests indicate that the experimental technique

itself is not responsible for the discrepancy between catalytic and

electrochemical experiments. It may be due to the appearance of small

amounts of new products caused by the presence of large amounts of chloride

ions, and born through the electrochemical mechanism. It is

156

Figure VIII-6 E / m V ( S C E )

157

TABLE V I I I - 2 .

c oupi e E°a /V(SHE)

E (pH 6) /V (SHE)

I2(5) + 2e~ = 2I~ 0.536 0.536 I2 (aq) + 2e~ = 2I~ 0.621 0.621 U + 2e~ = 3l" 0.536 0.536 HIO + H + + 2e~ = I~ + H20 0.987 0.964 2HI0 + 2H+ + 2e~ = I2 + 2H20 1.354 1.308 10" + 2H+ + 2e~ = I~ + H20 1.313 1.267 10" + Ha0 + 2e~ = I~ + 20H~ 0.49 0.49 2IC^~ + 2e~ =jl1~ + 2C€~ 1.19 1.19 2IC-ei + 2e~ = 12 + 4C/~ 1.06 1.06 HIO3 + 5H+ + 6e~ = I~ + 3H20 1.077 1.039 2 H I 0 3 + 1 0 H + + lOe" = I 2 + 6 H 2 0 1.169 1.123 IO3 + 6H+ + 6e~ = i" + 3H20 1.085 1.039 IOI + 3H20 + 6e~ = I" + 60H~ 0.26 0.26 2I0l + 12H+ + 10e~ = I2 + 6H20 1.195 1.140 H I O A + H + + 2e~ = I O 3 + H 2 0 1.603 1.58 HIO4 + 2H+ + 2e~ = HIO3 + H20 1.626 1.580 IOZ + 2H+ + 2e~ = IOI + H20 1.653 1.607 H5I06 + H + + 2e~ = IOI + 3H20 1.6 1.58 HC/O + H + + 2e~ = Cf + H20 1.50 1.48 C€0~ + H20 + 2e~ = 20H~ 0.89 0.89 C€ol + 6H+ + 6e~ = C€~ + 3H20 1.45 1.40 C/OZ + 8H+ + 8e~ = C/~ + 4H20 1.35 1.30

Source of data, reference 123, 25°C.

158

possible too that iodide is oxidised to products other than iodine,

although this is not borne out by the results in KN03 (Chapter VI).

Reaction between iodine and some impurity in the KC/ is another

possibility. Table 2 lists some electrochemical equilibria in which

iodine and chlorine species are involved. It must be considered too

that the good agreement between Ecat and Em points to homogeneous

removal of iodine rather than to participation of another electro-

chemical process at the catalyst. It should be said too that it is

highly unlikely that a mere change in the nature of the supporting

electrolyte (especially to KC/, electrochemically inert in the potential

range studied here) can bring about a change of mechanism at the

catalyst surface, or participate itself in the reaction.

b) Experiments on the Oxidation of Iodide.

It is unlikely that the reduction of Feic gives anything other than 32 33 36

Feoc. Indeed, electrochemical studies in KC€ 9 * have consistently

supported the occurrence of the simple overall reaction: Fe(CN) + e" ^Fe(CN)J~ (VIII-7)

Iodide and iodine, however, may in principle participate in a variety

of electrochemical reactions, many of which are listed in Table 2.

Some experimental work was therefore carried out to try to confirm

the existence of a product of the oxidation of iodide different

from I2, I3, and I2C/ , and to try to identify it. It is worth

mentioning here that the formation of complexes between iodine and

chloride ions is already considered in the apparent extinction

coefficient of I2 in 1 M KC€ solution, because of the way in which it

was measured (Chapter V).

159

Figure 7 shows the variation with time of the current when a KI +

KC/ solution is electrolysed at a constant potential of 293.0 mV, which

is close to E both in KC-f and in KN03 (oxidised platinum, Chapter Cul

VI). The KN03 experiment was carried out as a control. The fall in

current is due to the accumulation of the main product I3, which drives rev E^ towards more positive values and decreases the diffusion over-

potential according to eq. (1-47). Decrease in the I concentration

is insignificant, and makes no impact on the current. To describe the

temporal variation of the current, eq. (II-30a) can be integrated w.r.t.

[l3]. Noting that: i = 2FV d[I3]/dt

and introducing it into (II-30a), jl j is:

[Is] = 9[1 - exp(-t/(2FV(l/k - + 30/L -)))] 13 1

where 6 = [l~]3 exp[2f(E - E°) ]

The current is obtained from eq. (8) as:

(VIII-8)

(VIII-9)

(VIII-10)

i = i0 exp(-i0t/2FV9) (VIII-11)

where i0 is the current at t = 0*.

i0 = G/(l/k - + 30/L -) I3 -L (VIII-12)

The plots in Figure 7 were not corrected for the gradual decrease

in the volume of the solution. Both give straight lines, in agreement -4 -1

with eq. (11). The slope is around -1.3 x 10 s , close to a

calcula.ted one of -1.36 x 10 s for an initial volume of 0.250

The intercept at t = 0 is 505 yA in 1 M KN03, which is 9% higher than

the 462 yA calculated from eq. (12), but it is not clear why. The

160

time / min

Figure V I I I -7

Figure V I I I - 8

1.0

0.8

i m ~ 0.6

>0 DO

OA L I

20 40 ti me / min

[ I " ] 0 =1 .7 U M

1 M KCl

500 rpm

5° C

60

Figure V I I I - 9

161

current in KC/ is 13% higher at any one time than in KN03 in accordance

with the relative magnitude of the current observed in the i-E curves

(see previous section).

Comparison of the iodine produced during each of the tine intervals

between successive samples (as coulombs) and the electrical charge

simultaneously passed during the same time interval, is shown in Table

3. Account has been taken of the decrease in the solution volume to

calculate the " total charge remaining in the solution" , according to

eqs. (2)-(5). In KC€ 9.6% of the charge passed by the current fails

to form iodine (or tri-iodide), while in KN03 only 2.6% of iodine is

" missing" . If the first At is excluded (i.e., from t = 0 to t = 3 or

5 minutes) in order to avoid the uncertainty in the absorbance at t = 0,

the missing iodine in the remaining total charge passed is 8.5% in

KC/ and 0.5% in KN03. This confirms the suspicion that iodide produces

species other than I2 in the presence of KC^. It is interesting to

note that the amount of iodine produced in successive time intervals

in KC€, becomes closer and closer to the charge passed, thus suggesting

a cessation of the parasite reaction which in turn suggests that it

soon reaches equilibrium at that potential. However, these results

do not disprove homogeneous scavenging of I2.

Electrolyses at constant 0.500 mA of current were also carried out.

Figure 8 shows the [l2] vs. S^ [see eq. (VI-^ )] obtained in 1 M KN03 and in 1 M KC^. The slope furnishes a value of 0.508 mA in KN03, and

of 0.490 mA in KC/, which are ca. + 2% about the correct value. However,

in KC€ there is an initial 4-6 minute period during which the slope is

much lower. If the electrode is withdrawn from the solution, pre-

conditioned again according to Table VI-2, and the electrolysis continued

in the same solution, the induction period disappears, and the slope

162

TABLE VIII-3. ELECTROLYSIS AT CONSTANT POTENTIAL;293 mV (SCE),

0.05 M KI~, 500 rpm, 5°C, VG = 0.250 €, v = 0.005

Time Coulombs Passed (During At.) .1 of /min (1 M KN03) (1 M KCO

Iodine Charge Iodine Charge

3 0.083 0.101 5 0.123 0.148 7 0.102 0.131 10 0.146 0.143 11 0.111 0.127 15 0.140 0.138 0.118 0.123 19 0.116 0.120 20 0.126 0.133 23 0.097 0.116 25 0.133 0.127 27 0.116 0.112 30 0.121 0.122 31 0.102 0.108 35 0.094 0.117 40 0.127 0.112

Total charge remaining in solution3* 0.933 0.958 0.784 0.867

Including first time interval

continues to be equivalent to 0.490 mA. This proves that the parasite

reaction does not involve reaction with the platinum oxide, nor that

iodine was being retained on the surface. The latter explanation for

the induction period is unlikely for another reason. According to

Table 3, the apparent deficit in iodine formation is 0.083 C of charge, —1 —8 -2 equivalent to 8.6 x 10 mol of iodine atoms or 7 x 10 mol cm

-9 which is 35 times higher than the monolayer coverage of 2 x 10 mol -2 45 cm . Formation of layers of solid iodine do occur if [I ] > ca.

1 6 3

™"3 A 7 122 7 x 10 M, ' but only if i = L - because in this condition

[I ]a = 0 and the iodine formed at the surface of the electrode must

precipitate because its solubility is reached. In the 0.05 M KI used,

Lj- = 236 mA which is several hundred times greater than the current

employed.

In another test for adsorption, a 0.05 M KI + 1 M KC/ solution was

electrolysed for 55 minutes at 293.0 mV, at 50°C, a) = 500 rpm, and the

electrode withdrawn without switching to open circuit, spun in air and

rinsed with water. The absorbance of 10 ml of a 0.1 M KI solution at

the end of 5 minutes in contact with the electrode was 0.004, in a 4cm

cell. Had the missing iodine been adsorbed on the electrode surface,

and desorbed into the KI solution to form I3, the optical absorbance

would have been around 4.

Experiments were now carried out to try to detect the formation of

other oxidised iodine species such as 10 or I03, according to the

procedure outlined in Section VIII.2.c. During most of these runs,

the production of I2 was followed spectrophotometrically at 350 nm,

and the corrections in eq. (2)-(5) had to be applied. But continuous

sampling is not essential. Only one sample at the end of the electrolysis

suffices to establish the [l2].

If it is assumed that species of the general formula 10^ are produced,

treatment of the extracted solution (which still contains 0.05 M KI)

with acid, should produce iodine, according to: I0~ + (2p-l)I~ + 2p H~t ^pl2 + p H20 (VIII-13)

If it is also assumed that the reaction is quantitative, then the amount

of iodine produced by the acid is p times the amount of 10^ produced

during electrolysis. They need not be restricted to 10^, but it is

a possibility worth investigating. The results are shown in Table 4.

164

The first column shows the electrolysis time at constant current. The fifth column represents the mols of iodine mr\ produced in the

J-2

extracted solution by addition of acid. This and the previous two columns

refer to amounts in the volume of solution that remained at the end

of the electrolysis (usually 0.210 •£ if continuous sampling had been

carried out during electrolysis; 0.250 £ if not, as in the second entry) .

The number of equivalents were calculated according to eq. (6), taking

p = 1 in eq. (13). It is important to realise that the actual number

of coulombs employed in the electrolysis, given by It (t = electrolysis

time), need not be equal to the charge values in the third or the

fourth column, because some of it has been removed in the samples

(see also Section VIII.2.d.), except in the run (second entry), for

which i t is actually equal to the charge remaining in the solution

because only one sample was taken at the end of the electrolysis.

TABLE VIII-4. COULOMETRIC AND CHEMICAL ANALYSES. 0.500 mA, 0.05 M KI,

500 rpm, 5°C, 1 M KC/, V0 = 0.250^.

Electrolysis time /min

Volume remaining If

Total Charge Remaining in solution/Coulombs

107 irv e

/mol Number of equivalents^

45 0.210 1.233 1.316 2.9 2.8 48a 0.250a 1.374 1.440 0.76 9.0 60 0.210 1.572 1.715 2.7 6.0 30 0.210 0.774 0.849 5.8 6.4

No samples taken during electrolysis; Assuming thatrn = w [cf. eq. (6)];

J. 2 X Calculated from eq. (1);

^ Calculated from eq. (5); Q Calculated from the I2 released by the acid on the basis of " volume remaining" .

165

The results listed in Table 4 are quite irreproducible due to the

very small quantities of iodine (in the form of tri-iodide) produced.

The mean number of equivalents is 6 + 2.5 which leaves ample room for

choice among the several reactions listed in Table 2. There is also

the problem that more than one adventitious product might have formed.

Our experimental approach cannot tell this. A further point is that

if electrolysis is started in the presence of ca. 6 yM iodine, the

induction period disappears, and the rate of production of iodine remains

at 0.490 mA during the electrolysis.

In a more carefully controlled experiment, 1.73 yM I2 were added

to the KI + ¥£•€ solution and stirred at open circuit at 500 rpm, at 5°C.

The concentration of iodine fell slightly with time (Figure 9) over a

60 minute period. However, during the time elapsed between introducing

the RDE, switching on rotation, plus about 10 minutes to attain thermal

equilibrium with the bath, the concentration fell to 0.85 yM, which

decrease would have accounted for 0.043 C of missing iodine. This is

considerable (Table 4). This amount would surely increase as more

iodine is added to the solution because of a shift towards the product

side (unfortunately, no run was made without the RDE, so one cannot be

sure that this is due to catalysis by the platinum). Notice that a further

0.030 C over 50 minutes is accounted for by the 0.01 mA difference

between the applied 0.500 mA and the 0.490 mA production rate of iodine.

Since this difference is only 2%, it may well be due to a corresponding

error in the value of e^^, used in these calculations. I2

So it looks like an impurity in the KC/ was reacting with I2 produced

by the Feic + I reaction.

166

VIII.4. Conclusions.

From the results in Table 1 and Figure 2, it is clear that the

catalytic rate is in equilibrium at the catalyst surface; since the

isolated electrochemical couples are also in equilibrium at potentials

around the E value, the inescapable conclusion is Celt

that in KC^ too the reaction at oxidised platinum proceeds by the

electrochemical mechanism in the presence of KC/. However, this involves

the assumption of undisturbed overlap of the individual i-E curves in

the mixed system, which is not supported by the discrepancy between the

u' ^ and i /2F values. Alternatively, one could assume disturbed cat m J

overlap, but evidence of the latter is still wanting. No evidence was

detected of interference by iodide or iodine which might be irreversibly

adsorbed on the electrode on the reduction of Feic, but this does not

rule out interference by reversibly adsorbed species. It does not appear

likely that the Feic/Feoc couple could interfere with I oxidation.

But then, this situation would be similar to the one encountered on

reduced platinum (Chapter VII), in which (E . 2F u' ) differs from cat cat (E , i /2F) but remains on the I /l3 curve. This has not been observed m m here, but rather an intermediate situation in which E ^ = E , which cat m suggests that the reaction between I and Feic gives off iodine products

other than I3, I2> or I2C^ .

The electrolyses at constant current suggest formation of extra

iodine species. But they cannot tell whether they are of electrochemical

origin or formed by homogeneous reaction of iodine with some impurity

in the KC^ (the amounts involved are in the yM region). Failure of

Lambert-Beer's law at these low concentrations is possible too. Chemical

analyses of the electrolysed solution suggest the formation of some

oxidised form of iodine species.

167

The average value of the differencei /2F-u' is 2.7 x 10 ^ m cat mol s of iodine, or 0.094 C over 30 minutes period^ this is not

far from the difference Q r _ Q A = 0.075 C from the last entry in Table Kj A

4, which is a constant current electrolysis (0.5 mA is close to the

production rate of iodine during the catalytic run at 500 rpm; see

Table 1, 4th entry).

Therefore, it seems that most of the discrepancy between catalytic

and electrochemical data may be ascribed to events connected to the

I /I3 couple, therefore to the fact that the reaction is followed by

the appearance of tri-iodide.

168

CHAPTER NINE

CATALYSIS ON GLASSY CARBON

IX.1. Introduction.

It is known that carbons catalyse the reaction between ferricyanide 124

and iodide as well as several other redox reactions. However, the

electrochemical rate constants for ferricyanide reduction and for

the oxidation of iodide are considerably lower on carbonaceous elec-34 54

trodes like graphite and glassy carbon than on platinum. ' It

therefore seemed likely that the catalysis by carbon, unlike that

by platinum, will not be completely mass transport controlled. The

kinetics of reaction (1-1) were accordingly studied on a carbon surface

in order to test that part of the theory of redox catalysis in Chapter

II, which deals with irreversible or partly reversible charge transfer.

Glassy carbon was chosen for these studies because some information concerning the Feic/Feoc and I /I3 couples was available on this

34 52

material. ' Also, being harder than graphite, the surface of glassy

carbon is less prone to physical damage; if necessary, it can be

polished without great loss of material, which is an important consid-

eration if it must be done repeatedly. As mentioned in Chapter III,

it is an isotropic material (macroscopically), unlike graphite or

pyrolytic graphite, whose electrical conductivity depends on the

direction chosen for its measurement, i.e., along or across the

stacked planes.

169

IX.2. Experimental,

a) The Glassy Carbon RDE.

The electrode in Figure 1 was made of a D82-2 glassy carbon disk

(Vitrecarb, USA), 0.32 cm thick and polished on one side. Because it

possessed an irregular radius that gave it a slightly elliptical shape,

its circumference had to be smoothed so that its final diameter was

4.30 cm, instead of the original 5.1 cm, giving an apparent surface

area of 14.5 cm2. The non-polished side was glued to a stainless

steel former with conducting Araldite and both were squeezed inside a

niche of the same dimensions in a rod of heated vitrathene. The other

end of the rod had been hollowed and a thread carved in its inner wall

in order to be fastened to the complementary thread of the stainless

steel holder. The vitrathene was subsequently machined to a trumpet

shape around the disc. Care was taken not to scratch or touch the

polished surface during construction. As with the platinum RDE, the

holder was provided with a bakelite lining and nylon screws to avoid

electrical contact with the shaft of the rotation system, although the

holder itself is not in contact with the back of the electrode.

Electrical contact to the carbon was provided in exactly the same way

as with the platinum RDE (Chapter VI). The holder was painted with

white radiator enamel (International) and left to dry in the air without

baking it in the oven, although the construction was such that no metal

part ever came into contact with the electrolyte solution. There was no

actual need to paint the vitrathene as it is an inert polymer, but before

being used for the first time it was rubbed with Kleenex soaked in

acetone, and left in distilled water for several days. As with the

platinum RDE, the disk oscillated horizontally about + 0.5 mm around

170

glassy carbon

vitrathene

steel

bakelite

| 4.3 cm

6.4 cm

Figure IX-1

1 AN(1MH2S04 0.5M KNO-

2 h

1 1—

3 CAT(1MH2S0^)

4 5 CAH0.1M I^SO^)

6

0.05M K I 0.003 M Feic 5°C

- • 6

0.02 0.04 0.06 0.08 0.1

Figure IX-2 1//w (rpm)

1 7 1

a central position; some vertical displacement of the edge could be

descried distinctly and seemed larger than for the platinum electrode.

The maximum working speed was correspondingly lower: 1000 rpm, although

^max froin eq* i s ^ 1800 rpm (taking R = 3.2 cm, from the centre

of the electrode to the edge of the mantle). The vessel used for the

catalytic runs was 10 cm in diameter, which probably induced enhanced

stirring because the edge of this bigger electrode was closer to the

wall of the vessel.

A major flaw of this electrode was that eletrolyte crept at the

carbon disk/mantle contact line. The gap was not apparent to the

naked eye. It was only noticed when, after thoroughly cleaning the

electrode of a pink teecepol slurry, more of it appeared at the edges

upon pressing the edge of the mantle. It must be assumed that the

liquid reached the steel former. Thus, all the earlier work with this

disk was vitiated by this flaw. Once it was found, the electrode was

left overnight in distilled water to leach out the electrolyte and

remaining slurry from the cleft, dried in vacuum at room temperature,

and the cleft covered with yellow Humbrol enamel which sets at room

temperature. It was applied with the moistened tip of a needle to

avoid excessive spread of the paint. It was frequently renewed as it

tended to wear off after several polishings. -4 The manufacturers specify 30-80 x 10 -fl- cm as the electrical

resistivity for their glassy carbon, which leads to a total resistance -4 of about 1 x 10 ft across a disk of our dimensions; this is very small

-4 as 1 A would be required to produce 10 V drop across the electrode.

Typical currents in this work are in the mA range. The Araldite (RS,

silver loaded) used to glue the electrode to the stainless steel former

was of 500 yft cm specific resistance. Assuming a thickness of 0.01 cm,

the hardened glue contributed only ^ 10 ^ ft, across the 14.5 cm2 disk area.

172

b) Chemicals, Experimental Arrangement and Catalytic Runs.

The chemicals are described in Chapter V; the experimental arrange-

ment in Chapters V and VI. The potassium nitrate (AnalaR, BDH) was

recrystallised from distilled water (800 g KN03 + 1 t H20, heated to

70°C and filtered while hot through porosity 3 Quickfit sintered glass

filter; filtrate cooled to 5°C, crystals collected in the Quickfit

filter and washed with chilled distilled water; the recovery was about

70%). Aristar grade KI (BDH) was used. All runs were carried out in

distilled water. The supporting electrolyte was always KN03.

The volume of solution in the catalytic rates was 0.310 t, because

the larger electrode required the large 10 cm diameter Quickfit FV1500

vessel. With that volume of reaction mixture the electrode could be kept

about 1 cm below the surface of the solution, and about 2 cm above the

bottom of the reaction vessel.

Sampling was performed as described in Chapters V and VI, except

when high concentrations of iodine or ferricyanide were initially -4

present: for runs in the presence of 10 M I2, 2 ml samples were diluted

with 20 ml of 1 M KN03; with 5 x 10~5 M I2 or 5 x 10~3 M Feic, 5 ml

samples were diluted with 20 ml. In all runs, 10 samples were taken

one every 3 minutes, beginning at one minute after the start of the

reaction.

Except for uT values at a single rotation speed, all the errors C a L

quoted for parameters calculated by least squares fitting of data are

the standard deviations of the fitting itself, as defined in Appendix 4.

c) Pre-Conditioniong Procedures.

Several pre-conditioning procedures were tried until the catalytic

rate became reasonably reproducible. As in other chapters, the acronyms

CAT or AN indicate a final negative or positive potential (SCE),

173

respectively, in the sequence. The words in parentheses refer to the

solution (prepared in doubly distilled water), in which the pre-

conditioning was carried out. It was made at the temperature of the

subsequent catalytic run. After pretreatment, the electrode was

withdrawn from the cell and spun at high speed in the air while being

rinsed with distilled water. It is more convenient to discuss the

preconditioning in connection with the results obtained, and it is

therefore deferred to the results section.

The preconditioning cell itself had three compartments (Figure

VIII-1) separated by porosity 3 glass frits, so that the platinum CE

could be kept separated from the WE to avoid possible contamination of

the latter with platinum, which may affect the catalytic properties of 126

the glassy carbon. Nitrogen was always passed for 10-15 min through

the WE solution before each preconditioning.

IX.3. Results and Discussion.

A brief review will first be given of the results obtained for

several preconditioning procedures that were tried. They are vitiated

in some way by solution creeping at the carbon/mantle cleft, as imer,tioned

in the previous section. Probable effects are: corrosion of- the steel

former, especially during preconditioning in H2S0/» solution at anodic

potentials, diffusion along the cleft of the corrosion products and

deposition on the carbon outer surface upon application of cathodic

potentials (-0.700 V or -0.500 V (SCE) in some procedures). Here,

hydrogen evolution inside the gap is possible. Indeed, on occasions

after application of a cathodic potential, the open circuit voltage

(OCV) took about 20 minutes to reach +0.2 V (SCE), which seems reasonable

if hydrogen dissolved in the gap solution slowly diffuses away towards

174

the bulk of the solution. During the catalytic run, participation

of the Fe/Fe(II) couple at the steel former is conceivable, with

electron transfer taking place across the steel/Araldite/carbon

highly conductive phases. Several interfer ing redox reactions are >—«<

possible:

Fe + 2Fe(CN)T > Fe2+ + 2Fe(CN)e~ (IX-1)

followed by precipitation of Fe2[Fe(CN)6], and

Fe + U >Fe2+ + 3I~ (IX-2)

_l_ 126 The E° value for the Fe2 /Fe couple is -0.409 V (SHE), which makes 5 2+ these reactions likely. Although the Fe would be essentially

confined to the gap, it is difficult to estimate the magnitude of these

effects.

a) Preliminary Results.

Tables 1 and 2 define the AN (1 M H2S0A) and CAT (1 M H2S0*) pre-

conditioning procedures employed. The period at open circuit (OC)

was provided to allow the electrode to reach 0.20 V (SCE), an arbitrary

selected value.

TABLE IX. 1 AN (1 M H2S0z,) Procedure.

Potential/ Time a)/rpm V (SCE)

1.000 60 s 100

-0.700 15 s 0

1.000 10 min 100

175

TABLE IX.2 CAT (1 M H2S0J Procedure.

Potential/ V (SCE)

Time (o/rpm

1.560 2 s 100

1.000 60 s 100

-0.700 15 s 0

OC 10-20 min 100

Figure 2 shows a 1/u' vs. 1/cu2 plot for 0.5 and 1 M KN03 for Cat

both types of preconditionings. Figure 3 shows how E varied with CcL L

time under these conditions. The values of E at 10 minutes were cat arbitrarily chosen as representative of the run, and these are plotted

vs. a) in Figure 4 •

The non-zero intercepts in Figure 2 show clearly that the reaction

is not at equilibrium at the surface of glassy carbon. Moreover, the

E value at 10 min appear to vary with to, although they do not follow Cat

any obvious trend. The results show also that the type of preconditioning

has a marked effect on the rate and on E . This suggests that chemical cat groups on the glassy carbon surface formed during the preconditioning

participate in the reaction, either in the electron transfer act

(assuming that the reaction proceeds by the electrochemical mechanism)

or on the adsorbability of the species involved, or both. Since both

reactants are negatively charged, the rate must be very sensitive to

the charge of the surface groups. Predominance of positively charged

groups would tend to increase the rate, while the opposite would happen

with negatively charged ones. Marked increases in the rate were produced

176

00 >

E

348

346

344

342

340

338

344

342

340

338

336

AN (1 M HoS0.) L k

CAT (1 M H2S04)

0.05 M K I 0.003 M Feic 1 M KNO.

5" C U): as marked on each curve

334

J I L_ 12 16 20

time / min 24 28

Figure IX-3

177

I I I I I

0 200 400 600 800 1000 0) I rpm

Figure IX-4

178

when [KNO3J was doubled. As shown in Chapter VI, the difference between

the standard equilibrium potentials becomes less negative as

[KN03] increases (Table VI-10), which favours the catalytic rate

according to eqs. (11-17) and (11-22). The actual magnitude of this

effect depends on the term a2Z2rx in the exponential of eq. (11-17).

It is not clear why the line in Figure 2 corresponding to the

CAT (1 M H2SOi,) , 1 M KNO3, crosses all of the other lines and gives

a larger intercept. It will be seen later than even with preconditioning

procedures in which the conditions were more carefully controlled,

aberrant plots were occasionally obtained. The intercepts and slopes

of the lines in Figure 2 are listed in Table 3.

_2 TABLE IX.3 Dependence of u' on u> [equation (11-24) ].5 x 10 M KI, cat 3 x 10"3 M Feic, 5°C.

AN (1 M H2S0J CAT (1 M H2S0A)

[kno3J 0.5 M 1.0 M 0.5 M 1.0 M Q 00 - 1 10 u' /mol s cat 2.39 3.09 2.63 2.12 - 9 (*) - 1 10 bv /mol S (rpm) 2 21.1 16.7 18.3 9.91

(*): b = d(l/u' J/d(w 2) cat At this stage the CAT preconditioning was modified: it was carried

out in 0.1 M H2SOa instead and the potential programme is set out in

Table 4. The OCV at the end was only ca. 0.03 V (SCE) compared with

0.20 V in Table 2.

179

TABLE IX.4 CAT (0.1 M H2SO*) Procedure.

Potential/ V (SCE)

Time co/rpm

1.560 2 s 100

1.000 60 s 100

-0.500 5 min 0

OC 10-20 min 100

The catalytic rates obtained for several values of GO in 1 M KN03 are shown in Figure 2, and the corresponding line 5 is seen to agree with

the general trend of the other lines obtained with reduced electrodes.

However, a set of runs carried out some 6 weeks later under the same

conditions and with the same modified CAT (0.1 M H2S0<,) gave much

larger rates, plotted as line 6 in Figure 2. Increased rates after

prolonged periods of idleness were a recurrent feature in these early

experiments. The initial lower rates were never reproduced. This

trend almost certainly affects all of the results presented so far.

By this time the glassy carbon disk had lost some of its initial

glossyness. Examination with a magnifying lens revealed an irregular

surface, formed of very tiny lumps, probably a result of burning of

the electrode at 1.560 V (SCE) during preconditioning, and aerial

oxidation. The most obvious effect would be an increase in the surface

rugosity which would increase the real area available for the reaction.

These two phenomena could have also progressively eliminated impurities

accumulated at the surface during construction of the rotating disk.

Thus, reproducibility of the state of the surface cannot be achieved

180

by electrochemical preconditioning alone, in the case of glassy carbon.

Polishing of the electrode with grinding powder prior to electrochemical

treatment was therefore tried.

b) The correct polishing procedure was achieved by trial and error.

Initial trials involved rotating the disk in its shaft at c£. 100 rpm,

while hand-pressing on it with moderate strength a moistened cotton

wool ball (Booths Ltd., B.P. quality) sprinkled with some 0.3 ym

teecepol polishing powder (Abrafract Ltd., Sheffield). The ball was

made to go back and forth on the electrode over about 1 hour. This

treatment did not eliminate the tarnish on the surface. Examination

with the magnifying glass did not reveal any change in the appearance,

although the cotton had acquired a very dark tonality because of

material scratched from the carbon surface.

At this stage, creeping of the electrolyte into the carbon/mantle

gap was realised, and the flaw was rectified as described in Section 2a.

More drastic polishing conditions were also employed. The electrode was

rotated at 1000 rpm, and the cotton ball with the teecepol slurry was

pressed hard against the electrode in a back and forth movement for

another hour. This unfortunately produced concentric grooves on the

electrode, visible to the naked eye, and some very visible scratches.

The grooves and the tarnish, but not the scratches, disappeared upon

polishing for 1 hour with 25 ym alumina powder (Banner Scientific Ltd.,

Coventry) in the initial more moderate manner. Polishing the electrode

while it rotated on its shaft was not very convenient. Thus, the final

polishing procedure performed before every run was as follows. The

RDE was taken out of the shaft, throughly rinsed with distilled water,

placed face upwards on the bench, sprinkled with teecepol and rubbed

181

with a moistened cotton ball, as evenly as possible. Preferential

polishing in a direction or in a given area was minimised by frequently

turning the electrode, and by trying to vary the movement patterns

of the hand. The electrochemical treatment described in Table 5 or

in Table 6 always followed. In future reference to them, no explicit

mention of prior polishing will be made, but it must be understood that

it was carried out.

TABLE IX.5 CAT' (0.1 M H2S0A) Procedure.

Potential/ Time GO/rpm V (SCE)

1.000 1 min 100

-0.500 2 min 0

OC 10 min 100

TABLE IX.6 AN (0.1 M H2S0j Procedure.

Potential/ Time oo/rpm V (SCE)

1.000 1 min 100

OC 10 min 0

The OCV was ca. 0.20 V at the end of CAT1, and ca. 0.45 V at the end

of AN (0.1 M H2S0J .

182

c) Long Term Performance with AN (0.1 M H2S0A) Pretreatment.

Most of the work described in the remaining part of this Chapter

was carried out with this pretreatment over a period of ca. 17 weeks.

The performance of the glassy carbon rotating disk catalyst, judged

from the value of u1 ^ at 5°C, with 5 x 10~2 M KI, 3 x 10~3 M Feic, cat and 1 M KN03 at several co values, was periodically tested. The

1/u1 vs. I/to2 plots obtained are shown in Figure 5. The curves are Call

marked 1 to 4 in the order in which they were obtained. Line C was

obtained with the collected data of all the other curves. Table 7

gives the least squares parameters of each line, as well as the time

elapsed since beginning the runs with the polished catalyst and the

cumjjlative number of runs, in all sorts of conditions.

TABLE IX.7 LONG TERM PERFORMANCE OF GLASSY CARBON CATALYST

AN (0.1 M H2SOa), 0.05 M KI, 0.003 M Feic, 1 M KN03, 5°C.

Curve Number (w.r.t. Fig. 5) 1 2 3 4 C

9 oo 10^ u' _ / cat i - 1 mol s

5 . 2 1 + 0 . 39 6 . 4 3 + 1 . 1 5 . 1 3 + 0 . 77 5 . 5 9 + 0 . 74 5 . 6 2 + 0 . 9 2

1 0 " 9 b < * > / - 1 -L mol s(rpm)2

2.41+0. 2 2 3 . 4 0 + 0 . 39 2 . 4 4 + 0 . 45 2 . 4 6 + 0 . 34 2 . 7 5 + 0 . 4 1

Accumulated

Time/weeks 1 3 12 17 • -

Number of runs 8 38 96 1 1 0 -

(*): b = d(l/u' J/d(o) 2)

AN (0.1 M H

?SO^ 183

vO O

o s/ )0uiu)

,n / t

o

Figure IX-5

184

In spite of the long times involved in between, the plots show

no apparent trend towards increasing rates.

The value of E at 10 minutes for the AN (0.1 M H2S0i,) is shown cat in Figure 4 as a function of oo. The curves " 1" to " 4" correspond

to the respective " 1" to " 4" curves in Figure 5. No long term

trends are observed in this case either. These results and those in

Figure 5 must surely be due to the polishing of the catalyst which

produces a fresh surface every time, scratching off any irreversibly

adsorbed chemicals and impurities and obliterating any roughening

due to electrochemical preconditioning or to aerial oxidation of the

carbon. Thus, it is reasonable to assume that the curves will be

reproducible in the long term whatever the electrochemical treatment

following polishing.

However, the values of u' at fixed to show considerable scatter cat (Figure 5 and Table 8), perhaps because of traces of grease from the

fingers and from the cotton.

TABLE IX.8 CATALYTIC RATE AS A FUNCTION OF o).AN (0.1 M H2S0J

0.05 M KI, 0.003 M Feic, 1 M KN03, 5°C.

a)/rpm 100 150 200 300 500 750 1000 109 u' /mol s"1: cat Curve 1 2.27 2.77 2.67 2.81 3.38 3.63 3.80

2.31 2.60 Curve 2 1.91 2.10 2.65 3.09 3.02 3.68 3.68

2.12 2.46 Curve 3 2.08 2.77 2.84 3.34 3.05 3.38 3.57 Curve 4 2.42 2.39 3.07 3.23 3.28 3.97 Mean 2.2 2.5 2.8 3.1 3.2 3.6 3.8 + a 0.2 0.3 0.2 0.2 0.2 0.2 0.2

1 8 5

It is interesting to compare the values in Table 8 obtained with

the AN ( 0 . 1 H 2 S O a) with those in Figure 2 [AN ( 1 M H 2 S 0 ^ 1 M K N 0 3 ] .

The latter procedure gave catalytic rates 3-4 times lower than the

former. Since the electrochemical treatment was very similar, the

increased rates with AN (0.1 M H2S0z,) must be mainly due to the polishing

of the catalyst: roughening of the electrode and/or removal of adsorbed

films of impurities. In the absence of measurements of the real surface

area, changes in the latter remain conjectural. However, if this were

the only factor, E should have remained unchanged when passing from cat AN (1 M H2S0J to AN (0.1 M H2S0A) . In fact, E during runs with the cat latter was considerably less anodic (Figure 4). Moreover, the product

00 b u should be independent of the magnitude of the real surface area: ca u it is ca. 52 (rpm)2 for the AN (1 M H2S04) data (in 1 M KN03), and

ca. 15 (rpm)2 for curve C for the AN (0.1 M H2S0j data. The difference 00 in values is due to changes in the various kinetic parameters in u^at

and in b. The transport parameters a are not affected by the state j

of the surface. This interpretation is independent of the actual

mechanism of the catalysis. Assuming momentarily that the electrochemical

mechanism holds, then the increased catalytic rates and less positive

catalyst potentials would indicate that the AN (0.1 M H2S0<,) procedure

enhances the electrode kinetics of the I /I3 couple over those of the Feic/Feoc couple.

d) Comparison Between Oxidised and Reduced Catalyst.

Figure 5 also shows l/uf vs. l/u)* for reduced [CAT' (0.1 M H2S0A) ] cat glassy carbon. Comparisons should be made with curve C. The actual

values for the reduced catalyst are in Table 9. The least squares fitting

186

(3.21 + 0.30) x 109

The variation of

TABLE IX.9 CATALYTIC RATE AS A FUNCTION OF u. 5 x 10~2 M KI, Q

3 x 10 M Feic, 1 M KN03, 5°C, REDUCED CATALYST

[CAT1 (0.1 M H2S04)].

00/rpm 100 150 200 300 500 750 1000

109 u' /mol s"1 cat 2.27

2.48

3.00 3.17 3.47 3.80 5.00 5.29

Qualitatively, these results vindicate those obtained earlier without

polishing the catalyst (Section IX.3.a.). The rates with the reduced

catalyst are larger, and E less positive than with oxidised surfaces; cat This agreement suggests that the CAT' results are not uncharacteristic

despite the relatively few runs carried out and the scatter of the points.

The variation of E with time is shown in Figure 6. The difference cat in behaviour is striking: E for oxidised catalyst decreases with time cat while it increases for the reduced catalyst. From the values of if* in

Table VI-13, it is possible to calculate the equilibrium constant at

5°C for reaction (1-1) as 0.03432, and the equilibrium concentration of -4 total iodine is 1.921 x 10 M, for the initial conditions of

-2 -3 5 x 10 M KI and 3 x 10 M Feic in 1 M KN03; this furnishes 305.7 mV A (SCE) for the equilibrium potential of the mixture, E (i.e., E at

cat infinite time), upon application of eqs. (11-30). Therefore, one would

A expect E to change with time from its initial value towards E. In

-9 -1 produces u1 00 = (11 + 2) x 10 mol s , and b = cat — -1 -L -L mol s (rpm)2, which gives u' » b = 34 (rpm)2. Cau

E at 10 minutes with w is shown in Figure 4. Cal

187

.1000

o - o ANI0.1M H 2 S0 4 )

CAT'(0.1 MilijSO^ )

0.05M KI

0.003 M Feic

1 M KN03

5°C UMrpm): as marked on each curve

750

500

300

0 4

Figure IX-6 12

time I min 16 20 28

188

the case of the reduced catalyst, the initial potential is close to the A

equilibrium potential E in agreement with its fast catalytic rate. The

subsequent increase in E for the reduced catalyst is difficult to C e l t

explain, and may suggest that surface groups participate very actively

in the electron transfer process. Another characteristic of cathodically

pretreated disks is that E at a given time varies somewhat erratically

with a). By contrast, for the oxidised electrode, E decreases with cat time, faster at faster a) values. (That the initial fast decreasing

part is not due to slow homogenisation of the reactantssolutions is

shown by the fact that it is present even at the faster rotation speeds).

Equation (11-26), based on the electrochemical model, can be re-

written in the form

E = E°° (t) + a (t) u' /u)2 (IX-1) cat cat cat

This takes into account the fact that E and a vary with time due cat J

to the constant formation of the products, u1 too depends on time, cat but since the initial values are available for every oj, they will be

i the ones used in eq. (1). Thus, E was plotted against u1 /co

C a t C a L

according to this equation, one plot for each time, t, at which an

E reading had been made during the catalytic run, and fitted by least C a L

squares. Two such plots at t = 1 minute and 28 minutes are shown in

F igure 7 obtained with the oxidised catalyst and

with the reduced catalyst . These are straight lines in the case

of the former, but for the reduced one the points are too scattered for

linearity to be assured. The E00 (t) and a(t) values obtained were C a L

then plotted vs. time and extrapolated to t = 0 to obtain the initial

values to which the equation refers. The lines are shown in Figure 8

for a variety of experimental conditions. The extrapolated values and

slopes are listed in Table 10, together with data reported earlier for

u' ^ itself in Tables 7 and 9. cat

to c= —} rv

X I

i i i/)

> E

330 I s 1 min

325 h

320 r

315 h

310

305 -

300

( o . ) : AN (0.1 M H 2 S0 4 )

( 0 0 ) : CAT'(0.1 M H2S04

0.05 M K I 0.003 M Feic 1 M KNO.

0.01

u'cat

0.02

(nmol I s/rpm)

0.03

190

o—o AN (0.1 M HoS0. ) L k CAT' (0.1 M

0,05 M K I 0.003 M Feic 1 MKNO 5"C

w

28

Figure I X-8

12 16

time / min

20 2k

191

TABLE IX.10 KINETIC PARAMETERS AT u> = 0.05 M KI, 0.003 M Feic,

1 M KN03, 5°C.

AN (0.1 M H2S0J CAT' (0.1 M H2S04)

109 u' 00/mol s cat 5.6 + 0.9 11 + 2

E°° /mV (SCE) cat 341 + 1 331 + 1

-9 -1 — 10 b/mol s (rpm)2 2.8 + 0.4 3.2 + 0.3 -8 1 — 10 a/mol s (rpm)2 V -1.3 + 0.1 -0.90 + 0.03

TABLE IX.11 DEPENDENCE OF THE CATALYTIC RATE ON REACTANT CONCENTRATION.

AN (0.1 M H2S0Z,) PRECONDITIONING, 1 M KN03, 5°C.

(o/rpm 100 150 200 300 500 750 1000

103 [Feic ] /M 109 u' /mol s 1 (+0.05 M KI) cat

1.0 0.945 1.26 1.14 1.44 1.55 1.72 1.79

2.0 1.91 1.99 2.18 2.01 2.39 2.81 2.75

3.0 2.2 2.5 2.8 3.1 3.2 3.6 3.8

5.0 2.58 2.98 3.49 3.51 4.20 4.22 4.77

103 [KI]/M 109 u1 ^/mol s cat (+0.003 M Feic)

30 1.47 1.65 1.70 2.18 2.16 2.35 2.75

50 2.2 2.5 2.8 3.1 3.2 3.6 3.8

ioo a 3.34 3.55 3.53 4.16 4.14 5.25 5.08

200a 4.75 5.88 6.09 5.84 6.20 7.14 8.21

a [KN03J adjusted to give [K+] X 1.05 M

192

TABLE IX.12 DEPENDENCE OF KINETIC PARAMETERS ON THE REACTANT CONCENTRATION

1 M KNOs, 5°C.

103 [Feic] 103 [I ] 109u' oo cat E°° t (SCE) cat -9 10 b 10 8 a/ mol

/M /M /mol s /mV /mol 1s (rpm)2 V (rpm) 2

1 50 3.0 + 0.6 333 + 1 6.8 + 0.7 -2.86 + 0.03 2 3.4 + 0.3 338 + 1 2.4 + 0.6 -1.74 + 0.03 3 5.6 + 0.9 341 + 1 2.8 + 0.4 -1.3 + 0.1 5 7.4 + 0.6 345 + 1 2.4 + 0.2 -1.06 + 0.02

3 30 4.1 + 0.4 349 + 1 4.4 + 0.5 -1.82 + 0.03 50 5.6 + 0.9 341 + 1 2.8 + 0.4 -1.3 + 0.1 100 6.7 + 0.6 330 + 1 1.6 + 0.3 -0.89 + 0.03 200 9.8 + 1 318 + 1 1.0 + 0.2 -0.65 + 0.03

In the absence of electrochemical data and of knowledge of the changes

that may happen to glassy carbon surfaces following electrochemical

treatment, it is not possible to point out the reason for the increased

catalytic rates and decreased potential on the reduced catalyst. The

differences are certainly outside the experimental uncertainty. The

results indicate that the reducing treatment increases the reversibility

of the I /I3 couple relative to the Feic/Feoc couple.

In order to minimise the error due to long extrapolation when u1 ® ca l

is obtained from 1/u' vs. 1/co2 plots, it is best to work under cat conditions that give the smallest b u' Since this is 15 (rpm) 2 for cat the oxidised disk and 34 (rpm)2 for the reduced one, the oxidising

procedure AN (0.1 M H2S0A) was chosen to carry out the remainder of the

work. Another reason for this choice was the curious time-dependence

of E ^ observed for the reduced disk, cat

193

e) Dependence of the Catalytic Rate on the Reactant Concentration for

Disks Preconditioned by Polishing and AN (0.1 M H2S04).

The results are summarised in Tables 11 and 12. By plotting

In u' 00 vs. In C., the reaction orders were found to be 0.6 + 0.2 cat 2 ~ in [Feic] and 0.43 + 0.01 in [i ]. The uncertainty in the rates is

ca. + 10% (+ 0.1). Thus, if this is added to the quoted uncertainties

from the least squares fittings, the probably more realistic figures

are 0.6 + 0.3 in [Feic] and 0.4+0.1 in [I ]. Such large uncertainties

in these crucial kinetic parameters much reduce the value of modelistic

interpretation of the data. However, attempts to verify the electro-

chemical model may at least indicate if the values being obtained are

of the correct order of magnitude.

Assuming that the mechanism for I oxidation at glassy carbon in 61 the presence of Feic is that described by Wroblowa and Saunders on

graphite for which a = 0.5, Z = 1 and W - = 1, and that the reaction 56

of Feic follows the path proposed by Sohr, Muller and Landsberg on

graphite for which a = 0.2, Z = 1 and = 0.7, then ri and r2 may

be calculated according to eqs. (11-18) to be 0.71 and 0.29, respectively.

According to eq. (11-17), the catalytic reaction orders

[Feic], and r2W .- in [I ] would then be, respectively, 0.50 and 0.29.

This is not inconsistent with the experimental values, considering the

large errors in the uf 00 values. cat It is possible to show from eqs. (11-56) that, on assuming Tafel

region behaviour for the couples!

E°° = (r2/a2Z2f)ln(k2/kx) + (r2W_, /a2Z2P) ln[Feic ] - (r 2W_-/a2Z2f) ln[ i" ] cat Feic I (IX-2)

Figure 9 shows plots of E°° vs. In [Feic], and vs. In [i ]. The ca t -3 -2 slopes are (7+1) x 10 V and (1.6 +0.1) x 10 V, respectively.

194

350 r 1 M KNO-

l/l

> E

340

330

3 20

0.8 1.2

In [ Feic] /mM

3.4 3.0 4.2

Figure IX-9 In [ I"

4.6

I mM

5.0

)

5.4

I I I

C

2< C

2 'C

2

rev rev -,rev • „ rev

Figure IX-10

195

The calculated slopes using the parameters from the literature work 36 61 2 ,2 cited above ' are 2.4 x 10 V and 3.4 x 10 V, for Feic and I ,

respectively, in considerable disagreement with the experimental data,

although the orders of magnitude are the same.

The disagreement does not disprove the electrochemical model,

because the kinetics of electron transfer are likely to be complicated

by the simultaneous presence of the two couples, specially if both _ Feic and I are adsorbed. ' One must not discard the possibility

of adsorption of iodide on glassy carbon, even if it has not been found 61

to be the case on graphite.

In order to gain some insight into the kinetics of the Feic/Feoc

and I /I3 couples, the following calculations have been carried out on

the basis of the electrochemical model. The results offer some guidance

as to what to expect from electrochemical studies. Figure 10 shows

schematic i-E curves. If the concentration of one of the reactants,

say I , is kept constant, the crossing points of the curves describe the

i-E curves of the I /I3 couple as the concentration of the other reactant,

Feic, is varied. Thus, according to eqs. (11-56), by plotting In (2F uf ) vs. either at constant [I ] or at constant [Feic], cat cat one obtains the corresponding symmetry factors (l-ai)Zi and a2Z2.

This is illustrated in Figure 11. Moreover, eqs. (11-56) may be re-

arranged as:

ln(2F u1 «) - (1-ofx) Zif E« _ = ln(Fki) + W - ln[l"] (IX-3a) cat cat I

ln(2F u1 o?) + a2Z2f E°° = In (Ski) + W^ . In [Feic] (IX-3b) cat cat Feic

Therefore, by plotting the left hand side of eqs. (3) vs. the In of the

corresponding concentration, the electrochemical reaction orders W_. are

196

< E

8 m

0.6 r

0.2

S - 0.2

- 0.6 L

320

•—• 0.003 M Feic o - o 0.05 M K I

330 340

Ec°°at I mV ( SCE)

350

1 M KNO-

5 C

Figure IX-11

M KNO

3.4 3.8

Figure IX-12

0.8 1.2

I n[ Feic] / mM o-o)

4.2

In [ I' 1.6

/ mM 5.0

-1-23

- 2 4

-25

-2 6

2.0

5.4

=> bO ~n c

r-i -ttl 8

I P M

197

obtained. Such plots, based on the results in Table 12, are drawn in

Figure 12. The results from Figures H and 12 may be summarised as:

(l-ai)Zi = 1.8 a2Z2 = 0.64 (IX-4a)

W - =1.7 . = 0.76 (IX-4b) I Feic

Fkx = 1,09 x 10~12 A M-1'7 Fk2 = 7.87 x 102 A M~°'76 (IX-4c)

iooi = 6.7 x 10"3 A ioo2 = 0.76 A (IX-4d)

The iooj values were calculated for each couple from its definition in

eq. (I-18b), and the calculated quantities in expressions (4a) and (4c).

The quantities listed above (4a-4d) are not unreasonable, although

they do not agree with any of the mechanisms mentioned in Chapter III.

They probably represent various combinations of more fundamental

quantities related to the intimate workings of the electron transfer of

the couples under the particular conditions of this work. They reproduce

the experimental kinetic reaction orders and catalytic rates almost

exactly, which is a check on the consistency of the figures.

Further tests may be carried out with the slopes a and b in Table

10. According to eqs. (11-26) and (11-24), and since uf is used in cat place of i : m

a = (W^/c^- [I-] - WFeic/aFe±c[Feic])2 r2F/a2Z2f (IX-5)

b = 2F(r2WI-/aI-[l"] + rx W ^ / a ^ . j F e i c ]) (IX-6)

Therefore, plots of a[l ] or b[l ] vs. [I ]/[Feic] should yield straight

lines. They are shown in Figure 13. The scatter of the points is

considerable, and no clear-cut relationship emerges. Least squares

fitting to a straight line gives:

198

199

_7 - -1 — 10 a[I s V (rpm) 2 = -(0.4 + 0.1) - (0.016 + 0.003)[l ]/[Feic] (IX-7)

_ _ i -k 10 b[I ]/€ s (rpm)2 = (1 + 0.1) + (0.013 + 0.006)[I ]/[Feic] (IX-8)

The standard deviations arising from the fitting alone are substantial.

A full account of the errors should also include the error fittings of

a and b (Table 12) which are about + 10% of their absolute values

(see Table 12). Thus, no definite numerical tests can be meaningfully

carried out from eqs. (7) and (8). In spite of this, there seem to be

some patent inconsistencies with eqs. (5) and (6), e.g., the fact that

the slope in eqs. (7) and (8) is about two orders of magnitude smaller

than the intercept, while eqs. (5) and (6) predict roughly similar

values because all of the quantities involved are of about the same

size. It is possible to test whether it is the slopes or the intercept

that are likely to be correct. If one inserts into the appropriate

equations the a.Z. and W. obtained (4a) and (4b), and the a. values 3 3 3 3 calculated from the k. measured in Chapter VI (which are related through

the expression k_. = aja)2j where u> = 500 rpm; the resultant cr_. must then

be multiplied by 1.29, i.e., the ratio of the geometric areas

A (glassy carbon)/A(P t) V

then a % 104 € 1 s(rpm) 2 V and b * 5 x 105 € 1 s

(rpm) 2. The slopes of eqs. (7) and (8) are 3-10 times lar ger than

these values while the intercept furnished by eq. (7) is of a sign

opposite to that expected from eq. (5).

In spite of the large uncertainties in the figures, one should

not ignore these large numerical inconsistencies, in the sense that

this probably indicates that a more complex system than that considered

in Chapter II is at hand.

200

f) Dependence of the Catalytic Rate on the Concentration of the Products.

This is shown in Table 13. However, the data cannot be analysed

with plots of 1/u1 ^ vs. l/o)2 because eq. (11-24) is not valid in this cat situation:

TABLE IX.13 DEPENDENCE OF THE CATALYTIC RATE ON THE PRODUCT CONCENTRATIONS

5 x 10~2 M KI, 3 x 10~3 M Feic, 1 M KN03, 5°C.

oo/rpm 100 150 200 300 500 750 1000

103[Feoc]/M 109 u' /mol s 1 [ I 2 1 n = 0 cat t=0

0.1

1.0

1.54

1.92

1.69

2.50

2.25

1.66

2.21

1.92

1.82

1.72

1.91

1.66

1.74

1.46

i o 3 [ i 2 ] / m 109 u' /mol s 1 [Feoc] n = 0 cat t=0

0.05

0.10

2.02

1.84

2.29

2.01

2.39

2.16

3.11

2.46

3.19

2.92

3.17

3.32

3.72

3.21

the relatively significant product concentration would enhance the

contribution of the back electrochemical reaction; also, the Tafel

approximation is probably not valid for the couple whose product has been

added to the reaction.

This last point is clearly illustrated in Figure 14, where the over-

potential E -E. has been plotted as a function of time. E. was cat j j calculated from the Nernst equation (1-9) for each couple, using the bulk

concentrations of reactants and products. The latter were obtained from

201

the actual " total" values in eq. (V-14). No allowance was made for

the homogeneously produced substances, as E respond to their " total"

or net values, and not specifically to the heterogeneous component of

the overall rate.

As shown in Figure 14, the overpotential for each couple is in

the Tafel region (|ti| > 50 mV for I~/ll and > 100 mV for the Feic/Feoc)

during the first minutes of the reaction, and decrease steadily with time

due to accumulation of the products in the bulk of the solution. However,

if one of the products is present in significant amounts since the

beginning of the reaction, ri for the couple concerned is much reduced

right from the beginning, while the other couple still shows Tafel

behaviour and its r\ is not much affected, at least in these particular

conditions. Therefore, the catalytic rate is deprived of much of its

" driving force" , i.e., the overpotential of one of the

c o u p l e s , and therefore is greatly reduced in the presence of

the products. Because of the nature of the Butler-Volmer equation (1-16),

that describes the individual couples, a decrease in |n| not only

decreases the forward reaction, but correspondingly increases the back

reaction. The inference follows that if the catalysis proceeds through

the electrochemical path, then all products must have an inhibitory

effect on the catalytic rate, provided that their concentration is large

enough to decrease the overpotential of its couple. Quantitative

analysis of these effects is complicated by the fact that the Tafel

approximation cannot be used in one of the eqs. (11-56).

202

160 r

0,0 5 M K I 0-00 3 M Feic

1 M KNO ^

100 rpm , 5 0 C

no Feoc at t = 0

j = 1 ( l " /35 )

120

o—o I I 2 ] = 0

[ I 2 ] = 0.000 1 M

80

40 > E

D

J_

• •- •

12 16

time /min 20

•— •

24 2 8

- 40

- 80

- 1 2 0

- 1 6 0 j = 2 (feic / feoc)

Figure IX - K

203

g) Dependence of the Catalytic Rate on Temperature.

The data are shown in Table 14, and at infinite w in Table 15.

TABLE IX.14 DEPENDENCE OF THE CATALYTIC RATE ON TEMPERATURE. r\ Q

5 x 10 M KI, 3 x 10 M Feic, 1 M KN03, 5°C.

a)/rpm 100 150 200 300 500 750 1000

T/°C 109 u' /mol s 1 cat

5 2.2 2.5 2.8 3.1 3.2 3.6 3.8

15 1.48 1.59 1.81 2.14 2.67 2.88 2.75

1.72 2.23 2.21 2.46 2.81 2.94 3.05

25 1.54 1.40 1.63 1.93 2.10 2.33 2.31

TABLE IX.15 EFFECT OF TEMPERATURE ON THE CATALYTIC RATE AT u = » O Q

5 x 10 M KI, 3 x 10 M Feic, 1 M KN03, 5°C

T/°C Q 10 u1 00 cat /mol s

10 ) -1 -b/mol s(rpm)2

5 5.6 + 0.9 2.8 + 0.4

15 5 + 1 4.3 + 0.7

25 3.4 + 0.5 4.1 + 0.6

The Arrhenius plot of the data in Table 15 gives an apparent

activation energy of -4 + 0.1 Kcal mol \ The actual value of the

apparent activation energy is subject to large uncertainties as the

poor reproducibility at 15°C shows, but the decrease of u1 with cat increasing temperature seems genuine. This result does not contradict

204

the electrochemical model. If one uses eq. (11-17) to define a

Eapp = _ R = r 2 E a£i + TxESS? + a2Z2riAH° (IX-9) 3 9(1/T)

where the E^oj s are the activation energies of the standard exchange

current densities!

E?oj = -R 3ln iooj/a (1/T) (IX-10)

As shown in Chapter VI, the standard enthalpy change of the reaction AH°

is -7.72 Kcal mol . It seems likely that the exchange current densities

would increase with increasing temperature so that the E0oj values

would be positive. The overall balance in eqs. (9) could therefore be

of either sign. In the case of complete mass transport control (Chapter

VI), the net balance was shown to be negative in good agreement with

experiment.

IX. 4. Conclusions.

The results described in this chapter are concerned only with the

kinetics of the catalysis of reaction (1-1) on glass^carbon. Some

effort was devoted towards finding a suitable pretreatment of the electrode

that would furnish a stable long term performance of the catalyst.

Polishing with teecepol was effective in this respect, but the reproduc-

ibility was still not wholly satisfactory.

It was found that different electrochemical treatment following

polishing markedly affected the catalytic rate, which was twice as

fast on " reduced" glassy carbon than on ar 'oxidised" surface at a) =

The dependence of the catalytic rate and the catalyst potential on

concentration may be represented by equations of the form of eqs. (11-56)

in the Tafel region. The values of the different parameters required to

205

achieve such representation are quite plausible from an electrochemical

point of view, but they do not agree with any of the mechanisms which have

been proposed for the two couples in the literature. It is quite

possible, however, that the electrochemical parameters of each couple

are affected by the presence of the other couple, i.e., that undisturbed

overlap of the i-E curves might not hold for this system. The results

with the " reduced" and " oxidised" catalyst strongly suggests partici-

pation of chemical surface groups in the reaction.

The rate decreases upon raising the temperature. This is consistent

with the electrochemical mechanism according to eq. (11-17) since it has

been shown (Chapter VI) that the difference in the standard equilibrium

potentials becomes less favourable for the reaction.

A better understanding of the mechanism of this catalysis will

require a detailed study of the kinetics of the electron transfer of the

couples Feic/Feoc and I /I3 on glassy carbon electrodes.

206

CHAPTER TEN

SOLVOLYSIS REACTIONS

X.l. Acid-Base Catalysis.

a) Catalysis in solution by acids or bases involves proton

transfer to or from a reactant or an intermediate in the reaction.

The proton donor or acceptor " is said to be a catalyst in a homo-

geneous system when its concentration occurs in the velocity expression

to a higher power than it does in the stoichiometric equation" 128 (Bell). The step in question need not be rate-determining but

the fact that it occurs at all allows the appearance of a new low 129 + activation reaction path. If the reaction is catalysed by H or

OH only, the reaction is said to be subject to specific acid - base

catalysis. If any other weak acid or base, able to undergo acid-

base intercourse with the reactant, speeds up the rate too, then

general acid-base catalysis is said to be operative.

If proton transfer with the substrate, S> is the slow step in the I. 1 3 0 reaction, the rate v is given by s

v = k[S] (X-l) 130 The rate constant k is I

k = k0 + k +[H+] + kQH-[0H"] + I (kRX [HX ] + k x [X ]) (X-2) j J j

where HX_. and X_. are weak acids and bases, respectively. If only

specific catalysis is operative, then k = k =0. At very low HX. X.

3 3

pH values [OH ] may be neglected, and most of X will be protonated,

so that [X_. ] = 0. At very high pH, [H+] may be neglected, and

[HX_. ] = 0. Thus, k becomes:

207

k = k0 + kR+[H+] + I k R X [HX ]0 (X-3) j j

in very acid pH while for very alkaline pHI

k = k0 + kQH-[0H ] + I k x [HX.]0 (X-4) j 3 3

where the subindexed brackets refer to the stoichiometric concentrations

Then it is possible to obtain k + or k - from plots of k vs. [H+] or H OH [OH ], respectively. The intercept furnishes the rate constant, k0, of

the uncatalysed reaction plus the general acid-base componentj the

latter may be calculated if k0 is known, e.g., from runs in the absence

of the HXj s and X_. s. However, in order to prove that general acid-

base catalysis takes place it is necessary to show that the rate depends

on the stoichiometric concentration of the suspected catalyst, and not + 129 just on the equilibrium H concentration.

b) The Hydrolysis of Esters.

The hydrolysis of esters is an acid-base catalysed process. Current 131 textbooks list several proven mechanistic pathways. The acid

catalysis of simple esters is reckoned to follow the sequence!

0 kx

R—C—OR 1 + H (S) k-1

fast

OH II

R—C—OR'

OH

R—C—OR'

H20 R—C—OH fast R—C

I OH

OH

H20 slow

OH H

R—C—OR' I +

OH

+0H 2

K'

fast

+ R1 OH (X-5)

208

The rate v is given by:

v = (k2k,/k_1)[H+][S] (X-6)

However, in the case of t-butyl acetate, the stability of the t-butyl

cation allows another reaction path, which occurs simultaneously with 132 (5) J :

CH3C00C(CH3) 3 + H+ k l ^ [CH3C00HC(CH3)3]+ k-1

CH3COOH + (CH3)3C+ — H : z 0 > (CH3)3C0H + H+ (X-7)

This also leads to a rate law as in eq. (6). Path (7) contributes

> 80% in the 25-85°C temperature range.^^ The key step in the reaction

is the protonation of the acyl oxygen, which allows subsequent

nucleophilic attack by a water molecule. Acid catalysis should also

be effective if the proton is provided by a weak acid HX.

The OH ion is a nucleophile more powerful than H20 and it can

attack the acyl carbon without previous " sensitisation" of the 133 substrate :

CH3C02C(CH3) 3 + O H " — ^ — > CH3C02H + (CH3)3CO~ H 2° > slow

> CH3C02H + (CH3) 3C0H (X-8)

The rate is given by:

v = k 2[0H~ J[S J (X-9)

Other nucleophiles could act as catalysts too, but then the carboxylic

acid would not necessarily be produced. The carboxylic acid itself may

act as a catalyst if the reaction is subject to general acid catalysis.

209

In solutions around neutral pH, and in the absence of catalysts

other than H+ or OH l^O.

k = k0 + kR+ [H+] + kQH- ^/[H1-] (X-10)

The value of k passes through a minimum at a certain given by

dk/d[H+] = 0 = k + - k - K/[H+]2. (X-ll) H OH W min

+ 1 [ H ]

min " (k0H" V k H + ) 2 (X"12)

Introducing this expression into eq. (10)I

k,i. • k° + 2 ( V k0H" V * (X"13)

Taking-logio on both sides of eq. (12)

P ^ m - P ^ - I los-(k0H"/kH+) (x"14)

If a weak acid HY of total concentration A0 also catalyses the reaction!

k = k0 + kR+[H+] + kQH- K^/[H+J + kHyA0[H+]/(KHY + [H+]) (X-15)

If the dissociation constant K ^ is small compared with the prevailing

acidity, the general catalytic component will appear as part of the

uncatalysed reaction (k0 + k A0). If it is large, it will appear as HY part of the acid component (k + + k A0/|Q;however, in this case the H HY concentration of undissociated HY will be small and therefore its

catalytic effects small too.

210

c) Measurement of Rates.

The overall reaction of ester hydrolysis is!

R-COO-R' + H20 »RC00~ + H+ + R'OH (X-16)

In near neutral solutions it may be followed by continuously titrating + 134 the H produced with a strong base, in the so-called " pH-stat method" .

However, a correction must be made to the experimental data to allow for

the partial dissociation of the weak carboxylic acid. Let y stand for

the total acid produced (dissociated plus undissociated) at any time, t,

and let x represent the carboxylate concentration. Therefore I

y = [RCOOH] + x (X-17)

and also

[RCOOH J = [H+]X/Kd (X-18)

where Kp is the dissociation constant of RCOOH. Thus,

y = fx (X-19)

where

f = l + [ K + ] / K D (X-20)

From eqs. (6) and (9) it follows that the rate is first order in [Sj,

since the concentration of catalyst remains constant. One can therefore

write

In(a - y) = In a - kt (X-21)

where a is the initial amount of ester and y is given by eq. (17). In

order to relate the course of the reaction to the observed H+ produced,

x, eq. (18) must be introduced to give:

ln(a/f - x) = ln(a/f) - kt (X-22)

2 1 1

X.2. Displacement Reactions.

Displacement reactions are of the general form!

Y + RX >YR + X (X-23)

R is usually an alkyl group, X a halide, and Y the attacking nucleophile, i.e., a Lewis base, which may be either a polar molecule like water or

ethanol, or an anion like OH .

In S^l reactions (unimolecular nucleophilic substitution) the alkyl

halide dissociates relatively slowly into a carbonium ion and a halide 135 ion, followed by a swift attack by the nucleophile "" I

RX r~—> R+ + X" (X-24)

slow

R+ + Y > Products

The rate is expressed by:

v = k[RX] (X-25)

It is independent of the nucleophile concentration. Thus, if the

nucleophile is OH , the rate is independent of pH. If several nucleophiles

are present (say, water, ethanol and OH ion) they compete for the

carbonium ion, and there will be a mixture of products. In addition,

elimination of hydrogen may occur, producing alkenes.

Catalysis of S^l reactions by heavy metal ions of silver, mercury

and copper is well known; it is due to complexing with the unshared 135

electrons of the halide :

RX: — ^ > RX:Ag+ s 1 q w > R+ + AgX > Products (X-26)

Such solvolyses are also heterogeneously catalysed by solid silver halides 139 and by silver metal. The solvent for its part plays two important

roles: separation of the two ions, for which solvents with a high

212

dielectric constant are more suitable, and stabilisation of the ions

by solvation, which is easier in polar solvents than in less polar

ones. 1 3 6 1 3 7

The solvolysis of t-butyl bromide (t-BuBr) is an S^l reaction, '

which in ethanol and water mixtures proceeds according to:

H O/Et-OH — + (CH3) 3C-Br *-L±± ^ Br + H + (CH3) 3C-OH + (CH3) 3COCH2CH3 +

+ CH2=C(CH3)2 (X-27)

In such solvent mixtures the first order rate constant increases some

1000 times when the water content, i.e., one of the nucleophiles, is

increased from 10% to 60% v/v, in apparent violation of its S^l mechanism.

Actually, the water effects have to do with charge separation and ion 138

solvation, rather than with a change in the reaction path.

In S^2 reactions (bimolecular nucleophilic substitution) dissociation

of the alkyl halide does not occur! nucleophilic attack and loss of

the halide happen simultaneously! Y + R—X > YR + X~ (X-28)

The rate in this case is directly proportional to the nucleophile

concentration:

v = k[Y][RX] (X-29)

213

CHAPTER ELEVEN

AN INVESTIGATION OF NON-FARADAIC ELECTROCATALYSIS.

XI.1. Introduction. 140

Despic et al. have claimed that the hydrolysis of t-butyl

acetate (t-BuOAc) is accelerated by gold and silver electrodes when

their potential was pulsed by a square wave from the potential of zero charge (E ) in the anodic direction. As the ester does not pzc undergo charge transfer reactions in that potential region, and the

electrodes at open circuit did not significantly enhance the rate,

it was proposed that the electric field polarised suitable bonds on

the adsorbed ester in a way that facilitated hydrolysis. This mechanism

was termed " non-faradaic electrocatalysis" . Under their most

favourable experimental conditions on gold (0.5 M Na2S0<»; 40°C; electrode

area/solution volume ratio of 0.08 cm 10 1 M < [t-BuOAc] < 10 4 M;

pulses at 0.5 Hz between 0.25 V (E ) and 0.75 V vs. SHE; starting at pzc pH 6) they obtained a 27-fold increase in the first order rate constant

w.r.t. the homogeneous uncatalysed reaction.

The results of a study of non-faradaic electrocatalysis are reported

here. The reactions concerned are the hydrolysis of t-BuOAc in

0.5 M Na2S0z, on gold and silver pulsed electrodes, and the solvolysis

of t-butyl bromide (t-BuBr) in 80% v/v Et-0H/H20 on silver electrodes. 139

As metallic silver at open circuit catalyses the reaction, it seemed

pertinent to study the effect of pulsation in the hope that it would

enhance the catalytic rate.

214

XI.2. Experimental.

a) Chemicals.

The t-BuOAc (Aldrich) and t-BuBr (BDH) were purified by fractional

distillation. The middle fraction was collected and stored in the dark.

Prior to distillation, the t-BuBr was shaken with anhydrous Na2C03 and

filtered through No. 1 Whatman filter paper. Potassium hydrogen

phthalate (KHP, AnalaR), NaNC^ (AnalaR), Na2S04, and stock 0.5 M

NaOH solution (carbonate free) AVS, were from BDH. J. Burrough AR

ethanol containing 0.3% water was used without further purification.

All water was doubly distilled.

The ca. 0.02 N NaOH solution was prepared by diluting the stock

NaOH solution with de-aerated water inside a nitrogen-filled dry box.

It was titrated potentiometrically with 20 ml of ca. 0.001 N KHP

solution, which had been prepared by dissolving an accurately weighed

amount of ca. 0.1 g of the oven-dried salt (overnight at 100°C) in

500 ml of water. Titration was accomplished with the pH-stat equipment

described below, by automatic recording of the first derivative of the

titration curve.

The 80% v/v ethanol/water mixture was prepared by weighing 300 g

of ethanol, and adding 94.0 g of water.

b) Equipment.

A thermostat like the one described in Chapter V was used, except

that no cooling unit was necessary.

The solvolysis of t-BuOAc and t-BuBr produces one hydrogen ion per

reacted molecule of substrate (Chapter IX) . Thus, the reactions were followed

215

by titrating the H produced at constant pH with NaOH solution. The

pH-stat equipment in Figure 1 (Radiometer, Copenhagen), consisted of

a pH meter (PHM62), an automatic burette (ABU 12) provided with a

plastic reservoir bottle containing ca. 0.02 N NaOH, an automatic

titrator (TTT 60), and a recorder (REC 61) fitted with a derivative

unit (REA 260). It operates by delivering alkali if the pH drops

below a preset value. The volume of solution delivered is displayed

in the digital counter of the burette, and in the recorder chart as

a function of time; it can be operated automatically or manually. The

pulsing equipment consisted of a Farnell LMF 2 oscillator, which

supplied the square wave and operated at 1 Hz, connected to the

external input of a TR 70/2A Chemical Electronics potentiostat (0.3 ys,

rise time). The reaction vessel and electrochemical cell (Figure 2)

was a 50 ml straight walled, concave bottomed, pyrex glass Quickfit

vessel, containing a Teflon-covered magnetic bar, the latter actuated

by a submersible magnetic stirrer (Rank Brothers, Bottisham). Its

tightly fitting vitrathene lid was secured by six clamps to the

horizontal lip around the edge, and had enough holes to hold the delivery

tip for the alkali, the glass and saturated calomel electrodes, the

gold or silver working electrodes, and a short glass tube sealed with

a Beckman frit at the lower end and containing the coiled platinum

wire counter electrode. This tube was filled with supporting electrolyte.

Another lid with fewer holes was used for the homogeneous runs. The

electrodes and other tubing were tightly wrapped with PTFE tape at the

point of contact with the lid to avoid leaks of volatile material

during the runs.

216

Figure XI-1

Figure X I - 2

217

It was found that automatic operation of the pH-stat with

simultaneous pulsing of the gold or silver WE was not feasible, as

the pH meter readings fluctuated by + 0.2 pH units at roughly the same

frequency as the pulses. Manual operation was therefore adopted, with

the pH meter left in standby for, typically, 10-20 min during which the

pulses were applied. However, in order to keep the pH at a constant

value and to monitor the extent of the reaction, the solution was

regularly titrated during that time (every 5 min for t-BuOAc, 3 min

for t-BuBr) by briefly returning the WE to open circuit, reading the

pH and delivering enough alkali to restore the pH to its initial value

(the titration took 15-20 s; the total volume delivered up to that time

had to be written down). Pulsing was then resumed. To highlight the

effect of the electric field at the WE (either pulsing or constant

applied potential), potential-controlled periods were alternated with

open circuit periods. During the latter the solution was also regularly

titrated. The saturated calomel electrode was switched, from the pH

meter to the potentiostat and vice versa, according to the operation

being performed, which took an additional 40 s.

c) The Gold and Silver Electrodes.

The gold (1 cm x 1 cm) and silver foil (3 cm x 5 cm) electrodes

(Figure 2) were attached to a gold or silver wire, respectively. These

wires were soldered to a copper wire which was enclosed in a glass tube

and sealed in with Araldite. That part of the seal nearer the foil was

tightly wrapped with PTFE tape to avoid softening upon prolonged contact

with water.

Both electrodes were treated once by Despic's procedure : they were

first degreased in hot concentrated NaOH (a beaker half-full of NaOH

pellets with just enough water to cover them, and dissolved by vigorous

218

stirring), rinsed, briefly immersed in concentrated nitric acid, and

rinsed again. No apparent changes were detected in the gold electrode.

The silver electrode, initially grey, acquired a uniform white metallic

lustre, although it became appreciably thinner and brittle. Its lower

edge was badly corroded and had to be cut away with scissors, to give

the final dimensions quoted above. This treatment can thus be used only

once in the lifetime of the electrode. However, degreasing in NaOH was

occasionally carried out for both electrodes.

Before every run, the gold electrode was electrochemically pre-

treated in 0.5 M Na2S04 by holding it for 30 s at each potential of the

sequence 0.5, 0.0, 0.5, 0.0, 0.5 V (SCE). If a final reducing treatment

was desired, it was polarised in 1 M H2S0A for 30 s at 1.5 V, followed

by 30 s at -0.25 V (SCE). The electrode was then throughly washed and

used within a few minutes. The silver electrode was preconditioned by

holding it at -0.7 V (SCE) for 2 minutes in 1 M KN03. However, in some

runs this was omitted.

d) Experimental Procedure.

For the runs with t-BuOAc, either homogeneous or in the presence of

the gold electrode, 100 of the ester were injected quickly beneath

the surface of 100 ml of de-aerated 0.5 M Na2S04, and shaken for ca.

15 s at room temperature. This gave a concentration of 0.0075 M, o 127

calculated from the density of the ester at 25 C, and the volumes

employed. Then 50 ml were transferred to the reaction vessel, already

in position inside the thermostat, through the SCE holej this was

promptly plugged with the electrode, and stirring started. Previous 141 work by Dr. M.C.P. Lima had shown that if the ester was simply injected

into the reaction vessel already containing the supporting electrolyte,

it just collected at the surface, even under stirring, and volatilised

219

in the 4 ml dead space between the solution and the lid. Low rate

constants were then obtained. However, solutions prepared by shaking

between 5 s and 2 min led to a higher and reproducible value of the 141

rate constant. Lima also showed that passing nitrogen over the

surface of the reaction mixture during the run progressively depleted

the ester, and the rate dropped to zero because of evaporation of the

ester. It was therefore preferable to allow some air to be present

during the runs. However, the pulsing range used [0J5 to 1 .05 V (SCE) ]

is too anodic to cause electrochemical reactions of oxygen.

A different arrangement was used for runs in the presence of the

silver electrode, because at the very cathodic potentials employed here

[-1.0 to -0.5 V (SCE) ] oxygen is reduced. This is an undesirable factor

in studies of non-faradaic phenomena. Therefore, nitrogen was passed

through the supporting electrolyte in the reaction vessel for one hour,

with stirring. The nitrogen stream was then switched through a bubbler

flask immersed in the bath and containing pure t-BuOAc; nitrogen flow

and continuous supply of ester was thus provided. The ester concentration

in the reaction mixture soon reached an approximately steady state value

as it was removed by evaporation with the nitrogen outflow and by

hydrolysis. Because the resulting ester concentration was relatively

high, the experiments with silver electrodes were carried out at the

lower temperature of 35°C.

The initial unadjusted pH of the reaction mixture was ca. 5.4. If

the run was to be carried out at a more basic value a few of 0.5 M

NaOH were added with a microsyringe. If a more acid pH was needed, a

few microlitres of diluted (usually 1 M) H2S04 were added until the

pH dropped to the intended value.

220

The experiments with t-BuBr were carried out at 25°C in 80% v/v

ethanol/water mixtures containing 0.3 M NaN03, chosen as supporting

electrolyte because of several possible inorganic salts quoted in the

literature it was the most soluble in this solvent mixture. Fifty ml

were placed in the reaction vessel, thermostated and nitrogen passed

for at least 1 hour under stirring. During this time the pH slowly rose

and stabilised at ca. 8.5. Nitrogen was then allowed to pass over the

surface for the rest of the run. The reaction was started by injecting

beneath the surface 50 of a mixture of 20 y/ of t-BuBr in 1 ml -4 pure EtOH, to give a substrate concentration of 1.8 x 10 M.

e) Treatment of Experimental Data.

The laboratory data are the volumes of alkali delivered, x (in y O ,

up to given times, t. Thus it is convenient to express the initial amount

of ester, a, in eq. (X-22) as y/ of NaOH solution, according to the

formula:

a/y^ = 106 vp/M[NaOH] (XI.1)

where v is the volume of ester (ml) in the 50 ml reaction mixture, p

its density (g cm 3) and M ibs molecular weight (g mol the [NaOH]

is that of the titrant delivered by the ABU12 (mol .

The hydrolysis rates of t-BuOAc were corrected according to section

X.l.c., and equation (X-19). This correction required values of the

dissociation constant of acetic acid (K^) in 0.5 M Na2S0z,. It is known

that the temperature dependence of K0, both in zero ionic strength (y)

and in concentrated solutions, is given by

log - log K0 = -p(t - 6)2 (XI.2)

221

where t is the temperature in degrees centigrade and K^ and 0 are constants

independent of t but dependent on y", p equals 5 x 10 ^ irrespective 1 of

y or t. The values of K and 0 in water (y = 0) were calculated from the 0

data of K^ at several temperatures by Harned and Owen and are listed in Table 1. 142 TABLE XI.1 IN WATER.

t/°c 45 50 55 60

105 K^/mol f'1 1.670 1.633 1.589 1.542

By plotting log (105 Kp) + pt2 vs. t, the values found were 0 = 29.34°C,

105 = 1.715 (r = 0.9996). K^ at higher temperatures obtained by

extrapolation were:

TABLE XI.2 IN WATER.

t/°c 6 5 7 0 7 5

10 5 Kp/mol 1.483 1.419 1.350

Data for Kp in Na2S04 were not available. Therefore K^ and 0 in

0.5 M Na2S04 (y fy 1.5) were assumed to be equal to the values in 1.5 M 142

NaC/ solutions. Data are available for 1 and 2 M NaC^ solutions,

and values for 1.5 M NaC- were obtained by linear interpolation (Table 3).

TABLE XI. 3 DATA IN 1 M KC^.

Y -log K Q 0

1 . 0 1 4 . 4 9 5 7 3 5 . 7

1 . 5 4 . 5 3 2 4 A 3 9 . 4 A

2 . 0 1 4 . 5 8 7 5 4 5 . 0

a Interpolated value.

222

The values of K calculated from eq. (2) are then given in Table 4.

TABLE IX.4. ESTIMATED VALUE OF Kp in NaC^ (y = 1.5)

t/°c 35 40 60 70

105KD/mol t'1 2.94 2.93 2.80 2.64

A list of f values calculated from eq. (X-20) is shown in Table 5, for 141

conditions appropriate to the work carried out here and by Lima.

TABLE XI.5. CORRECTION FACTORS f, UNDER VARIOUS EXPERIMENTAL CONDITIONS

Medium t/°c pH f

WATER 60 6.40 1.03 65 6.40 1.03 70 5.50 1.22 70 6.40 1.03 70 7.00 1.00 70 7.50 1.00

70 8.30 1.00

75 6.40 1.03

0.5 M Na2S0* 40 5.44 1.12 60 4.07 4.0 A 60 4.12 3.71 60 4.45 2.27 60 4.81 1.55 60 5.25 1.20 60 5.44 1.13 60 6.40 1.01 60 7.62 1.00 60 >_ 8. 00 1.00

223

The [H+] values in eq. (X-20) were estimated from [H+] £ 10~pH,

which will differ somewhat from the true concentration because of lack

of knowledge about the activity coefficient of H+ and because the pH

measurements include the liquid junction potential between the saturated 143

KC^ solution of the SCE and the reaction mixture. However, it can be

seen from Table 5 that above pH 6.40 the correction factor, f, may

almost be ignored in the calculations and that it exceeds 1.20 only

below pH 5.5.

f) Extracts from Despic' et al.'s"^^ Experimental Procedure.

" t-BuOAc was hydrolysed in 0.5 M Na2S0*, starting at pH 6, at constant

temperature in an inert atmosphere"

" Hydrolysis was carried out in a closed glass vessel, thermostated

by an ultrathermostat to 0.01°C. The lid [of the vessel] had provisions

for inlet and outlet of inert gas and for taking out samples for titration.

It also served as a support for the three electrodes: the gold plate

electrode, a saturated sulphate reference electrode connected to the

former via a Luggin capillary and a counter electrode. The latter was

a gold wire enclosed in a glass tube with a glass frit at the end through

which it was filled with electrolyte upon immersion and which served as

electrolytic junction with the bulk of the solution. Titrations of

the acid formed were made with the standardised NaOH solution (0.00063 M)

in the usual way with potentiometric end-point determination. "

"In a typical experiment 100 ml of the aqueous Na2S0z, solution were

placed into the cell, thermostated to a desired temperature [30, 35 or

40°C] and freed of dissolved oxygen by bubbling inert gas [nitrogen].

Ester was then added to form a solution of the initial concentration in

224

-4 -1

the range of 10 - 10 M. Samples of 2 ml were taken out at time

intervals of 20 min and the acid titrated. After some 200 minutes the

solution was heated to 70°C for half an hour and the acid titrated

again as to establish the final value after hydrolysis is completed."

XI.3. Results and Discussion,

a) Homogeneous Runs with t-BuOAc.

The first order rate constant k was calculated from plots of

ln[a/ f-x J vs. t, according to eq. (X-22). Good linear plots were obtained

(Figure 3) although they curve at long times probably because of slow

evaporation of the ester. The rate constants obtained under several

experimental conditions (but in the absence of gold or silver electrodes)

are listed in Table 6.

The reproducibility in the automatic mode was better (+ 0.2%) than

in the manual one (+ 1-2%); the latter also gave k values some 3-6% lower.

As expected from the acid/base catalysis of this reaction, k passes

through a minimum at about pH 6. The log k values are plotted vs. pH

in Figure 4 . The rate constants obtained from first order plots not

corrected for the partial dissociation of acetic acid are also shown.

These give the wrong impression that the reaction is inhibited at acid

pH values. The value of k at pH 6.40 in 0.5 M Na 2S0/, (auto mode) of

-3 -1 0.291 x 10 min is markedly higher than that in water in the same

-3 141 conditions, 0.240 x 10 , obtained by Lima. This larger value could

be due to a combination of factors such as catalysis by the HSO/, ion

and changes in the activity coefficients of the reactants (ester and

129—131

hydrogen ion) and of the activated complex (the primary salt effect )

or to changes in the pKa of the alkyl-bound oxygen in the ester (the

secondary salt effect).

225

o ro z

9.74 6

9742 h

9.736 h

3=19316^.1 NaOH (0.0075 M t-BuOAc)

t = 1.13

0.5 M NajSO >H 5.44

6 0 ° C

manual mode

PH Figure X I - 1 0

226

TABLE IX.6 RATE CONSTANT IN 0.5 M Na 2S0 4,0.0075 M t-BuOAc, 60°C.

pH 10* k/min" 1 Method

4.07 0.461 manual

4.12 0.507 manual

4.45 0.404 manual

4.81 0.340 manual

5.25 0.302 manual

5.43 0.264 auto

5.44 0.267 auto

5.44 0.276 manual

5.44 0.272 manual

6.40 0.272 manual

6.41 0.290 auto

6.41 0.291 auto

6.41 0.291 auto

7.62 0.300 manual

8.00 0.316 manual

8.50 0.349 manual

9.00 0.552 manual

9.30 0.948 manual

Analysis of the data according ti

in Figure 5 . Assuming that the value

in pure water applies to the data in

data are obtained!

-3 -1 k 0 = 0.29 x 10 min

k + = 2.5 M _ 1 m i n " 1

H

-3 -1 k 0 = 0.27 x 10 min

k^ T T- = 3.8 M 1 min 1

eqs. (X-3) and (X-4) is shown

of K = 9.61 x 1 0 1 4 M 2 at 60°C w

1.5 M N a 2 S 0 4 at 60°C, the following

from k vs. [ H + ]

from k vs. 1 / [ H + ]

227

228

These values are probably affected by the SCE/0.5 M Na2S0*, liquid

junction potential and by the fact that, in ideal conditions, the pH

furnishes the value of a „ + , not [H +]. The k + value is considerably H H

-1 -1 o higher than 0.82 M min found by Adam, et al. in 0.93 M HC/ at 60 C.

If it is assumed that the difference is due to catalysis by the HSO*

ion, its rate constant can be estimated from eq. (X-15) as*.

(2.5 - 0.82) M " 1 m i n " 1 . 0.5 M _ _ -1 . -1 k u c - = = 1.7 M min

H S 0 * 0.5 M

where A 0 = [Na2S0<»] = 0.5 M and lCr0n~ (the dissociation constant of the

HbU

HSOz, ion) has been taken as 0.5 M for an ionic strength of 1.5 at

o 10c 144 25 C. ' The actual value for k „ 0 - is probably smaller, once salt HbUz, effects have been eliminated. Indeed, it should be smaller than k +.

H

However, this appears to be the first evidence to show that this hydrolysis

is subject to general acid/base catalysis, and not just to specific +

catalysis by H and OH .

The value for k_ - at 6.6°C is 0.0248 M _ 1 m i n " 1 , 1 4 5 and 0.1082 at Url

25°C. 1 3 3 This leads to a value of 1.09 M _ 1 min" 1 at 60°C, well below

the value in 0.5 M N a 2 S 0 A . However, it is the result of a long extra-

polation, and therefore subject to considerable error, but it neverthe-

less suggests that the presence of Na 2S0z, might be having a catalytic

effect on the rate.

The value of k reported by Despic et a l . 1 4 ^ at 40°C in 0.5 M Na2S0<,

-4 -1 at an initial pH of 6 is 2.1 x 10 min , which is ten times higher than

the value of 2.9 x 10 min 1 found by L i m a . 1 4 1 A value of 1.7 x 10 min 1

132 can be estimated for k in pure water from Adam et al.'s data. Thus

229

Despic's data are out by a factor of 10. Lima has found that heating

the ester at 70°C (Section XI.2.f) leads to only 6% of ester hydrolysed,

whereas Despic, et al. assumed that half an hour at 70°C caused complete

hydrolysis. Their a values were therefore much too small, and this

would have given them abnormally high homogeneous rate constants since

in the early stages of the reaction kt x/a.

b) Hydrolysis of t-BuOAc in the Presence of Gold and Silver Electrodes.

Figure 6 shows a typical run with the gold electrode at 60°C. Its

presence at open circuit (marked OC) does not modify the rate.

Application of various pulsing rd[imes at 1 Hz (a: 0.25-0.75 V; b: 0.15-

0.65 V; c: 0.35-0.85 C; d: 0.25-1.05 V, vs. SHE) did not affect the

rate either. Under our experimental conditions, rate increases of 15 / f

times w.r.t. the homogeneous value were expected according to Despic s

data. Table 6 suggests that enhancements as small as 50% (i.e., a factor

of 1.5-fold) would have been detected as an increase in the slope

during the pulsing period. Instead, the whole run can be described -3 -1 by a smooth line with a slope of 0.291 x 10 min , very similar to the

homogeneous rate constant. The slight curvature was probably caused

by slow evaporation of the ester, as the run lasted for nearly 3 hours.

Figure 7 shows that on silver too, pulsation between -0.75 (E ) pzc

and -0.25 V (SHE) at 35°C did not enhance the rate, although 70-fold 140

increase in k would have had to occur in these conditions. Runs

with silver had to be carried out at pH 9. At lower values, application

of pulses actually led to apparent negative rates, i.e., the pH actually

went up rather than down. It was probably caused by electrochemical

reduction of residual oxygen or of water:

oc

230

OC OC b

OC 0 C

i - 9.870

V

h 9.662

Au electrode

\ Hz

a: 0.2 5 - 0.75 V ( S HE) b: 0.1 5 - 0.65 " c : 0.3 5 - 0.85 " d : 0.2 5 - 1/05 ii H

b 9.854 o TO

\

9.846 Z

h 9.83 8

0.5 M Na 2 S0 4 , pH 5.4 4

60° C

0.0075 M t - B u O A c

r 9.830

I I I I i 1 1 1 1

0 20 4 0 6 0 8 0 100 120 140 160 time / min

Figure X I - 6

231

OC

-o -o

o ro

70

60

50

40

30

20

10

0

OC

Ag electrode

pH 9.00, 0.5 M Na2S0^ ,35 • C

0.0 3 M t - B u O A c

1 Hz a : - 0 . 2 5 0.75 V (SHE)

12 16 20 24 time / min

3 2 3 6

Figure X1-7

i t i i I 1 1

5.0 5.4 5.8 6.2 6.6 7.0 7.4

PH

Figure X I - 1 0

232

02 + 2H20 + > 4OH (XI-4)

H20 + e~ > j H2 + OH" (XI-5)

In case these negative results were due to impurities preferentially

adsorbed on the electrodes, or to C-f ions leaked from the SCE, the runs

were repeated with the following precautions: the Na2SO*, was carefully

recrystallised (155 g plus 400 ml water, heated to 95°C, filtered while

hot, cooled at 5°C, precipitate recovered by filtration, rinsed with

chilled water and dried at 160°C for 18 hours). The SCE was replaced

with a Radiometer K601 mercurous sulphate reference electrode (MSE).

It had a potential of +0.2199 V vs. SCE at 60°C. The mV scale of the

pH meter was calibrated by reading the pH of various NaOH dilutions

in 0.5 M Na2S04 with the glass/SCE pair, and the corresponding mV with

the glass/MSE pair. Calibration curves at 27°C (room temperature) and

at 60°C are shown in Figure 8. The 27°C calibration was used for all

runs. Another point to consider is that Despic et al. did not mention

the use of stirring during their runs. Stirring should have speeded

up any diffusion-controlled steps in the catalytic process and so, if

anything, have increased the effect of pulsing. However, as an extra

check, the run with the gold electrode was carried out with discontinuous

stirring. The stirrer was operated only for 8 min at the beginning of

the run to achieve thermal equilibrium with the bath and thereafter only

during the short peroids in which the acid produced was being titrated.

The resulting plot at 60°C for the gold electrode is shown in Figure 9 ,

with no effect being caused by pulsation at 1 Hz between 0.25 and 0.75 V

(SHE). Figure 10 shows a run at 60°C with the silver electrode,

with the usual continuous mechanical stirring, but with recrystallised

salt and MSE, which shows that pulsation does not seem to have any effect

233

OC OC

9.76 0 o TO

9.75 0

9.740

9.73 0

Figure X I- 9

Au electrode pH 5.44, 6 0 0 C 0.5 M Na2S04

0.0075 M t - B u O A c

1 Hz a: 0.25 - 0.75 V ( SHE)

no ester ester present

0 C OC 0 C

-o OJ XJ T3

•JZ o ro Z

400

300

200

100

Ag electrode pH 9.00, 6 0 ° C

0.5 M Na2S04

0.003 M t - B u O A c

1 Hz a: -0.25 -0.75V ( S H E )

N2 switched through ester f l a s k

2 0 4 0 60

time / min

% 0 100 120

Figure X I - 1 0

234

c) Homogeneous Runs with t-BuBr.

The results of the homogeneous solvolysis of t-BuBr in 80% v/v

Et0H/H 20 are summarised in Table 7.

TABLE XI.7 HOMOGENEOUS SOLVOLYSIS OF t-BuBr 80% v/v Et0H/H 20, 25°C.

Medium pH 10 4 k/s 1

no salt 8.50 3.58

no salt 8.50 3.63

no salt 8.50 3.65

0.3 M NaN0 3 7.95 3.63

0.3 M NaN0 3 8.70 2.96

0.3 M NaN0 3 8.00 3.83

0.3 M NaN0 3 8.80 3.83

0.3 M NaN0 3 8.70 3.83

The values of k are somewhat scattered but they confirm that the rate

constant is independent of pH (Chapter X). The presence of 0.3 M

NaN0 3 exerts only a small increase in k as would be expected from an

uncharged reactant. The rate constants in the absence of the salt are

-4 -1

close to the value of 3.58 x 10 s in the same conditions reported

elsewhere.

d) Solvolysis of t-BuBr in the Presence of Gold and Silver Electrodes.

The presence of the gold electrode at open circuit did not affect

the rate. Pulsing was not tried because the aim of this section was to

study pulsing effects when the metal by itself catalyses the reaction.

235

o ro

5.8

H 5.6 tz

5.2 L

10

Figure X I - 1 1

20 3 0 time I min

Ag electrode

pH 8 . 8 0 , 2 5 ° C

0.3 M NaNO.

1 80|lM t - B u B r

-0 .70 V ( SHE) 1 Hz a: -0 .20

4 0 5 0 —I

60

5.4

5.2 L

0 10

Figure X I - 1 2

simulated run

_l

2 0 30 4 0

time I min

236

In the presence of the silver electrode at open circuit (no salt -4 -1 present) the rate constant rose to 5.7 x 10 s . Silver is known

to catalyse this reaction through adsorption of the alkyl halide by 139 its bromide end. In the presence of 0.3 M NaN03 the rate constant

-4 -1 decreased to 4.5 x 10 s probably due to competitive adsorption

of the N03 ions. After repeated use of the silver electrode as a -4 -1

catalyst, the rate constant stabilised at 4.20 x 10 s

As Figure 11 shows, pulsation at 1 Hz between -0.7()and -0.20V (SHE)

actually decreases the rate constant (catalytic plus homogeneous) to

negligible values. During the subsequent open circuit period, the rate -4 -1 constant increased again but stayed at 2.47 x 10 s , well below its

homogeneous value. Holding the potential at constant values [Ex = -0.45 V

and then E2 = +0.05 V (SHE)] is seen to reduce the rate constant again,

but less than during pulsing. In a separate run, the rate was apparently

brought to a halt when a constant potential of -0.7 V (SHE) was applied.

At the same time some 0.3-0.4 mA were observed to flow through the

counting resistor. The subsequent rate constant on open circuit was -4 -1 again only 2.47 x 10 s

It is possible that the apparent decrease in rate might have been

to reactions (4) and/or (5) or to N03 reduction. In fact, if the observed

current produces one OH ion per electron, it would be equivalent to - 8 — —1 -1 + 6-8 x 10 mol OH -6 s The rate of H production after ca. 15 min -4 of reaction (a = 1.8 x 10 M t-BuBr) is*.

r a t e = -d[t-BuBr] = _a k (_kt) (XI_6) dt

—8 + —1 —1

or 5.2 x 10 mol H ^ s , which would be almost completely " titrated"

by the current, if a reaction like (5) is taking place.

237

That the rate did not return to its open circuit value on removal

of the polarising potential can be shown to be a mathematical artifact.

For suppose that the electrochemical reaction has removed b molar H +

ions from the reaction mixture. Then the concentration of acid formed

by the solvolytic reaction and neutralised by NaOH will seem to be only

x', where x' = x-b. It is thus ln(a-x') that will be plotted against

time to give the first order rate constant. However, it follows from

eq. (X-21) that:

- l e t

ln(a-x') = ln(a-x + b') = ln(a e + b) (XI-6)

so that the slope of the plot will be k? = -d ln(a-*T) = a k_e~kt < k (XI_?)>

a e + b

Figure 12 simulates this behaviour. The open circles represent

the open circuit overall rate (homogeneous plus heterogeneous) calculated -4 -1

from eq. (X-21) using a = 450 \i€ and k = 4.2 x 10 s , which are

typical of these runs. The filled circles represent the plot calculated

according to eq. (6), with b = 61 \i€, i.e., the volume of NaOH that

failed to be delivered to the reaction mixture during the 10 min period of pulsation (horizontal section). The final rate constant is 2.86 x -4 -1

10 s , well below the homogeneous value and close to that obtained

experimentally.

238

XI.4. Conclusions.

None of the experiments reported here, whether with t-BuOAc at

gold or at silver electrodes, or with t-BuBr at silver electrodes, has

provided any evidence for the phenomenon of non-faradaic electrocatalysis.

The experimental technique used here is very similar to Despic et al.'s

and some of the differences were examined in special experiments. As 141

shown by Lima their homogeneous rate constants are 10 times too

high, almost certainly because they used erroneously low values for

the total ester concentration, a. Their catalytic rate constants are

probably out by the same factor. It is difficult to estimate these rate

constants, as Despic', et al.'s model requires diffusion of the ester

towards the electrode, adsorption,charging of the double layer and

bond polarisation)desorption of the products away from the electrode

and discharge of the double layer. Any of these steps may be rate

determining. However, it is possible to estimate the maximum possible

rate by assuming it to be equal to the frequency of pulsing, and based on

complete coverage of the electrode. A Leybold molecular model of the O 2 t-BuOAc molecule was found to project an area of some 50 A on a flat -9 2

surface, which leads to a maximum coverage of 2.7 x 10 mol on the 8 cm

gold electrode used by Despic. We shall assume that all these adsorbed

molecules react at the moment of switching the potential from 0.25 V

to 0.75 V (SHE), since according to the model put forward by Despic no

further adsorption of ester should take place at 0.75 V, because it is —8 —1 —1 so far away from the E . This leads to a rate of 5.4 x 10 mol 4 s , y pzc

because Despic's solution volume is 0.1 € and the whole pulse lasts

0.5 s under their most favourable conditions. From Table 2 in Despic's

paper, k % 2 x l 0 4 s 1 a t 40°C, which leads to initial rates of 2 x 10

239

mol € 1 s 1 when [t-BuOAc] = 10_1 M to 2 x 10 8 mol / 1 s 1 at 10 4 M.

These rates should be reduced by a factor of 10 to account for the -6 -9 error m the initial ester concentration, giving 2 x 1 0 - 2 x 1 0

mol € 1 s Thus, at the higher ester concentrations, Despic's initial 2

rates are higher than the maximum possible rate by a factor of up to 10 ,

Another test of their pulsed rates can be made by examining their

activation energies E^ between 35 and 40°C. Taking only the values for

gold electrodes pulsed between 0.25 and 0.75 V (SHE) at frequencies, v,

of 0.5 or 1 Hz, we have

v/Hz R E^/k cal mol"1

l*<o

0.5 1 41.6 mean of Table 2

1 1 51.6 from Table mo 0.5 9 42.5 from Table 1

Here R is the ratio of the periods during which the electrode was held

at the lower and at the upper potential limit for each pulse. Despic'

et al. themselves quote a figure of 39.9 kcal mol 1 without specifying

the frequency regime. Such enormous activation energies are far larger

than one would expect for a heterogeneously catalysed process. Further-

more, they are at least ten times greater than the activation energy

for any diffusion-controlled process. These high temperature coefficients

are very hard to reconcile with the large magnitude of the reported

catalytic rate constants themselves.

No genuine effects of changes in the interfacial electric field

at the silver electrode on the catalysis of the t-BuBr solvolysis could

be found. t-BuBr is a polar molecule so that its degree of adsorption

on the electrode would be expected to be influenced by the field,

and hence the catalysis by silver. It could be, of course, that these

effects are small and were masked by the other faradaic effects. In

240

any case, no significant non-faradaic electrocatalysis appears to

operate in this case either.

We remain at a loss, however, to account for the qualitative

differences between the work reported here and Despic' et al.'s. Following

a conversation with Professor Despic, and from their published experi-

mental procedure [reference 140 and Section XI.2.f.], it seems that his

student, Mrs. Ivic", was not aware of the experimental problems associated

with the high volatility of the t-BuOAc. Thus, the much higher rates

she obtained by pulsation could be due to her plugging all of the holes

in the lid of the reaction vessel with the various electrodes, thus

reducing evaporation; these holes would presumably remain unplugged

during homogeneous runs in which no electrodes are needed, thus allowing

most of the ester to volatilise and leading to an apparently far lower

rate. However, this hypothesis does not explain why their rate constants

on pulsed gold electrodes have a maximum around the Ep2C» Professor Despic

has told us that further work to try and resolve the discrepancy is

being carried out in his laboratory, and his results are awaited with

interest.

241

APPENDIX THREE

SIMULTANEOUS HOMOGENEOUS AND HETEROGENEOUS RATES

The Setting: The Feic + I reaction on platinum RDE and in the bulk of

solution.

Qualitative Description: The reaction comes almost to equilibrium at the

platinum surface (Chapter VI). Therefore the catalytic rate is completely

controlled by the concentration gradient across the diffusion layer (DL).

The homogeneous reaction must contribute to this gradient; hence the

catalytic rate is affected. The purpose here is to try to evaluate the

extent of these homogeneous effects.

Semi-Quantitative Description: Because of the variation of the concentration

of reactants and products in the DL the homogeneous rate R^ varies along

it. At x = 0, R^ = 0 because of the equilibrium condition; at * >_

R^ = R^ (the bulk value of R^). Using Fick's second law:

3C. 3 2C. dj " V A (A1"»

where v. is the stoichiometric coefficient (v. > 0 for reactants; and < 0 3 3

for products). R^depends on all Cj(x) (thus eq.(1) represents a system

of n coupled differential equations), and its full dependence is required

to solve (1). We do not know this dependence. To estimate the

homogeneous effect, it will be assumed that R^ varies linearly inside the DL:

242

A steady state will be assumed so that 3C./8t = 0. Because of (2), it is 3

now enough to solve only one equation. Take j = I3, v_. = -1. Then:

D82CAx2 + (RN 6J* = 0 (Al-3) H N

Integrating once from * = 0 to X = X!

DOC/8X) - Fa + (R^/26n)X2 = 0 (Al-4)

where Fa = DOC/3X)v . Integrating again from = 0 to * = 6 *.

A—(j N

D(Cb - Ca) - F°6n + R ^ / 6 = 0 (Al-5)

Then*. "cat = " = {C° ~ c b ) D A / 6 N " V 7 6 (A1"6)

where is the apparent catalytic rate, which includes the homogeneous cat b

contribution inside the DL. C is the bulk [l3] from homogeneous and

catalytic origin. Therefore, the first term on the extreme right hand

side term in (6) is not the 'true' catalytic rate u . A6„ is the volume cat N of the DL so that the second term on to the right is insignificant

compared to the first. However, for the sake of completeness a relation

between and the observed value u°^S (in mols per second) will be obtained.The cat cat overall rate u^ (homogeneous plus catalytic) is!

UT = Ucat + (A1"7)

where V* = V - A6>t ; V = volume of solution. V' is used instead of V N because includes the homogeneous contribution inside the DL. But cat by definition [Eq. (II-7)]!

* obs u , = u . cat cat

2 4 3

Therefore*.

C I - ucat + (V - v > 4 - (C° - Cb)AD/aN - 7 A ^ / 6 (Al-9)

The second term is still small. Thus!

uobs _ uapp _ o _ cb ) A D / 6 (A1.10) cat cat N

If Cb is expressed as a contribution of catalytic origin plus another

((£) of homogeneous origin a

obs Arx h/J6 (Al-11) = u - ADC / 6W cat cat H *

If is evaluated at t = 0, at which C^ = 0, then u°^S = u , and cat ' H ' cat cat no homogeneous effect will be observed.

244

APPENDIX THREE

The following computer programs fits by least squares a set of

N pairs of data (X, Y) to the parabola:

Y = Al + (A2)X + (A3)X2

PROGRAM P0LYN2

00100 DIM X(15), Y(15) 00105 X1=X2=X3=X4=P1=P2=P3=P4=P5=Y1=Y2=Y3=A1=A2=A3=A4=S=0 00110 PRINT "ENTER NUMBER OF DATA POINTS" 00120 INPUT N 00130 PRINT "ENTER DATA AS X, Y" 00140 FOR 1=1 TO N 00150 INPUT X(I), Y(I) 00160 NEXT I 00170 FOR 1=1 TO N 00180 X1=X1+X(I) 00190 X2=X2+X(I) **2 00200 X3=X3+X(I)**3 00210 X4-X4+X(I) **4 00220 Y1=Y1+Y(I) 00230 Y2=Y2+X(I) *Y (I) 00240 Y3=Y3+(X(I)**2)*Y(I) 00250 NEXT I 260 Xl-Xl/N 261 X2=X2/N 262 X3=XB/N 264 X4=X4/N 265 Y1=Y1/N 266 Y2=Y2/N 267 Y3=Y3/N 00270 P1=Y2-X1*Y1 002#0 P2=Y3-X2*Y1 00290 P3=X2-X1**2 00300 P4=X3-X1*X2 00310 P5=X4-X2**2

0 0 3 2 0 A 3 = ( P 1 / P 3 - P 2 / P 4 ) / ( P 4 / P 3 - P 5 / P 4 )

0 0 3 3 0 A 2 = P 2 / P 4 - ( P 5 / P 4 ) * A 3

0 0 3 4 0 A 1 = Y 1 - A 2 * X 1 - A 3 * X 2

0 0 3 5 0 F O R 1 = 1 T O N

0 0 3 6 0 S = S + ( Y ( I ) - A 1 - A 2 * X ( I ) - A 3 * ( X ( I ) * * 2 ) ) * * 2

0 0 3 7 0 N E X T I

0 0 3 7 5 S = S Q R ( S / ( N - 1 ) )

0 0 3 8 0 P R I N T " A L = " ; A L

0 0 3 9 0 P R I N T " A 2 = " ; A 2

0 0 4 0 0 P R I N T " A 3 = " ,* A 3

0 0 4 1 0 P R I N T " S = " ; S

0 0 4 1 2 A 4 = A 2 * ( 1 0 * * ( - 7 ) ) / ( 6 0 * 0 . 2 1 )

0 0 4 1 5 P R I N T " I N I T I A L R A T E = " J " M O L A R P S E C O N D "

0 0 4 2 0 P R I N T " A N O T H E R R U N ? "

0 0 4 3 0 I N P U T Q

0 0 4 4 0 I F Q = 1 T H E N 1 0 0

0 0 4 5 0 E N D

246

APPENDIX THREE

The following computer programme solves numerically eqs. (11-31) and

(11-32) for i (as v ), and calculates E from eqs. (11-30) for the m cat m 93 Feic/I system by the Newton-Raphson method, under the conditions stated

on lines 100-160 in the program.

PROGRAM CATRATE 00100 REM 00110 REM THIS PROGRAM CALCULATES THE INITIAL CATALYTIC RATE AND 00120 REM THE MIXTURE POTENTIAL BETWEEN FERRICYANIDE AND IODIDE 00130 REM ON A SMOOTH ROTATING PLATINUM DISK ELECTRODE OF 11.2 CM 00140 REM SQ., AT 500RPM, 5 DEG. CETN., IN 1M POTASSIUM NITRATE, 00150 REM IN A VOLUME OF 0.210 LITERS. 00160 REM 1 IS FOR FEIC, 2 FOR FEOC, 3 FOR TRI-IODIDE, 4 FOR IOD 00170 PRINT " ENTER MILLIMOLES/LITER OF" 00180 PRINT " FEIC, IODIDE, FEOC, TRI-IODIDE" 00190 INPUT CI, C4, C2, C3 00200 PRINT " ENTER RATE ESTIMATE IN UNITS OF NMOLAR/SECOND" 00210 INPUT XI 00220 Xl=4.053E-5*X1 00230 M=0.00178389 00240 L1=2.665E-3*C1 00250 L2=2.425E-3*C2 00260 L3=0.006588*C3 00270 L4=4.717E-3*C4 00280 IF L1>L4 THEN 00310 00290 P=L1 00300 GOTO 00320 00310 P=L4 00320 F=(L3+X1)*((LQ-X1)**(-3))*(((L2+X1)/(Ll-Xl) ) **2) 00330 D=F*(2/(L2+Xl)+l/(L3+Xl)+3/(L4-Xl)+2/(Ll-Xl)) 00340 X2=X1+(M-F)/D 00350 IF X2<P THEN 00380 00360 Xl=(Xl+P)/2 00370 GOTO 00320 00380 IF ABS(1-F/M)>1E-10 THEN 00480

247

00390 IF ABS(1-X1/X2) >1E-10 THEN 00480 00400 E=0.02396*LOG((0.001*Cl-X2/2.665)/(0.001*C2+X2/2.425)) 00410 E=0.2598+E 00420 PRINT 00430 X3=2.467E-5*X2 00440 PRINT 11 RATE=" ;X2;" MOLAR/SECOND" 00450 PRINT 00460 PRINT " EMIX=" ;E', 11 VOLTS VS. SCE" 00470 GOTO 500 00480 X1=X2 00490 GOTO 00320 00500 END

The following computer programme solves numerically eqs. (11-31) and (11-32) for i (as u' ) and calculates E from eqs. (11-30) for m cat m the Feic/I system. The method used is that of halving successively the interval where i is known to belong, under the conditions stated m

on lines 100-140 in the program.

PROGRAM OEDIPUS 00100 REM THIS PROGRAM CALCULATES THE INITIAL CATALYTIC RATE AND 00110 REM THE MIXTURE POTENTIAL UNDER TOTAL MASS TRANSPORT CONTROL 00120 REM OF THE REACTION BETWEEN FERRICYANIDE AND IODIDE AT A 00130 REM PLATINUM RDE OF 11.2CM SQ, 500 RPM, 5 DEGREES CENT., 00140 REM 1M POTASSIUM NITRATE 00150 REM 1=FERRICYANIDE, 2=FERR0CYANIDE, 3=TRI-IODIDE, 4=I0DIDE 00160 M=0.00178389 00170 PRINT " ENTER NUMBER OF CALCULATIONS TO BE DONE" 00180 INPUT N 00190 FOR 1=1 TO N 00200 PRINT " ENTER MILLIMOLES/LITER OF" 00210 PRINT " FEIC, IODIDE, FEOC, TRI-IODIDE" 00220 INPUT CI, C4, C2, C3 00230 L1=2.665E-3*C1 00240 L2=2.425E-3*C2 00250 L3=6.588E-3*C3 00260 L4=4.717E-3*C4

248

00270 IF Li<1.4 THEN 00300 00280 X1=L4 00290 GOTO 00310 00300 Xl=Ll 00310 X2=0 00320 X3=X1/2 00330 F=(L3+X3)*((L4-X3)**(-3))*(((L2+X3)/(L1-X3) ) **2) 00340 IF ABS(F/M-l)<1E-10 THEN 00360 00350 GOTO 00490 00360 IF ABS(X2/X3-1)<1E-10 THEN 00380 00370 GOTO 00490 00380 E=0.02396*LOG((0.001*Cl-X3/2.665)/(0.001*C2+X3/2.425)) 00390 E=0.2598+E 00400 A=5.18135E-6*X3 00410 B=4.6262E-7*X3 00420 PRINT 00430 PRINT " RATE=" ; A; " MOLES/SECOND" 00440 PRINT " =" ; B; " MOLES/SECOND CM2" 00450 PRINT 00460 PRINT " EMIX=" ; E; " VOLTS VS SCE" 00470 PRINT 00480 GOTO 00570 00490 X2=X3 00500 IF F<M THEN 00530 00510 P=-l 00520 GOTO 00540 00530 P=1 00540 X3=X2+(P/2)*ABS(X2-X1) 00550 X1=X2 00560 GOTO 00330 00570 NEXT I 00580 END

249

APPENDIX THREE

The following computer program?fits a set of N pairs of data (X,Y)

to a straight line

Y = B + MX (A4-1)

by the least squares method. The standard deviation of intercept, W,

and of the slope, Z, are defined as!

W =

and

Z =

I [ B- (YJ - MX^R/CN-L) 1/2

(A4-2)

J [M-(Y. - B)/X.]2/N-l 14

1/2 (A4-3)

respectively. In the case of eq. (3), pairs (X., Y.) for which X. = 0 3 3 3

are rejected by the program.

PROGRAM LMS 00100 PRINT " ENTER NUMBER OF DATA POINTS" 00110 INPUT N 00120 P=N 00130 PRINT " ENTER DATA AS X,Y" 00140 FOR 1=1 TO N 00150 INPUT X,Y 00160 S1=S1+X 00170 S2=S2+X**2 00180 S3=S3+Y 00190 S4=S4+Y**2 00200 S5=S5+X*Y 00210 IF X=0 THEN 00280 00220 S6=S6+1/X 00230 S7=S7+X**(-2) 00240 S8=S8+Y/X 0 0 2 5 0 S 9 - S 9 + ( Y / X ) * * 2

00260 T=T+Y/(X**2) 00270 GOTO 00290 00280 P=P-1 00290 NEXT I

0 0 3 0 0 M = ( N * S 5 - S 1 * S 3 ) / ( N * S 2 - S 1 * * 2 )

0 0 3 1 0 B = ( S 3 - M * S 1 ) / N

0 0 3 2 0 R = ( N * S 2 - S 1 * * 2 ) / ( N * S 4 - S 3 * * 2 )

0 0 3 3 0 R = M * S Q R ( R )

0 0 3 4 0 W = S 4 - 2 * M * S 5 - 2 * B * S 3 + S 2 * ( M * * 2 ) + 2 * M * B * S 1 + N * ( B * * 2 )

0 0 3 5 0 W = S Q R ( W / ( N - L ) )

0 0 3 6 0 I F P < 2 T H E N 3 9 0

0 0 3 7 0 Z = P * ( M * * 2 ) - 2 * M * S 8 + 2 * M * B * S 6 + S 9 - 2 * B * T + S 7 * ( B * * 2 )

0 0 3 8 0 Z = S Q R ( Z / ( P - 1 ) )

0 0 3 9 0 P R I N T

0 0 4 0 0 P R I N T " Y = " ; M J " X + " ; B

0 0 4 1 0 P R I N T

0 0 4 2 0 P R I N T " C O R R E L A T I O N C O E F F . = " ; R

0 0 4 3 0 P R I N T " S T D . D E V T N . O F I N T E R C E P T = " ; W

0 0 4 4 0 I F P,<2 T H E N 4 7 0

0 0 4 5 0 P R I N T " S T D . D E V T N . O F S L O P E = Z

0 0 4 6 0 G O T O 0 0 4 8 0

0 0 4 7 0 P R I N T " S T D . D E V T N . O F S L O P E C A N N O T B E C A L C U L A T E D "

0 0 4 8 0 E N D .

251

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